diff --git a/.dockerignore b/.dockerignore
index 7809863ef32862b2d609df896c09dd23c23073f0..8eb1e4df8a9fea82a6e291a6e1b4472d34f51f9d 100644
--- a/.dockerignore
+++ b/.dockerignore
@@ -4,8 +4,12 @@
 # things to include
 !docker
 !synapse
+!rust
 !README.rst
 !pyproject.toml
 !poetry.lock
+!build_rust.py
+
+rust/target
 
 **/__pycache__
diff --git a/.github/workflows/release-artifacts.yml b/.github/workflows/release-artifacts.yml
index ed4fc6179db39b332ab1b026ce8d818b13292a3d..0708d631cd368749336f0c80f50a257e9d577fae 100644
--- a/.github/workflows/release-artifacts.yml
+++ b/.github/workflows/release-artifacts.yml
@@ -15,7 +15,7 @@ on:
 concurrency:
   group: ${{ github.workflow }}-${{ github.ref }}
   cancel-in-progress: true
-  
+
 permissions:
   contents: write
 
@@ -89,9 +89,67 @@ jobs:
           name: debs
           path: debs/*
 
+  build-wheels:
+    name: Build wheels on ${{ matrix.os }}
+    runs-on: ${{ matrix.os }}
+    strategy:
+      matrix:
+        os: [ubuntu-20.04, macos-10.15]
+        is_pr:
+          - ${{ startsWith(github.ref, 'refs/pull/') }}
+
+        exclude:
+          # Don't build macos wheels on PR CI.
+          - is_pr: true
+            os: "macos-10.15"
+
+    steps:
+      - uses: actions/checkout@v3
+
+      - uses: actions/setup-python@v3
+
+      - name: Install cibuildwheel
+        run: python -m pip install cibuildwheel==2.9.0 poetry==1.2.0
+
+      # Only build a single wheel in CI.
+      - name: Set env vars.
+        run: |
+          echo "CIBW_BUILD="cp37-manylinux_x86_64"" >> $GITHUB_ENV
+        if: startsWith(github.ref, 'refs/pull/')
+
+      - name: Build wheels
+        run: python -m cibuildwheel --output-dir wheelhouse
+        env:
+          # Skip testing for platforms which various libraries don't have wheels
+          # for, and so need extra build deps.
+          CIBW_TEST_SKIP: pp39-* *i686* *musl* pp37-macosx*
+
+      - uses: actions/upload-artifact@v3
+        with:
+          name: Wheel
+          path: ./wheelhouse/*.whl
+
   build-sdist:
-    name: "Build pypi distribution files"
-    uses: "matrix-org/backend-meta/.github/workflows/packaging.yml@v1"
+    name: Build sdist
+    runs-on: ubuntu-latest
+    if: ${{ !startsWith(github.ref, 'refs/pull/') }}
+
+    steps:
+      - uses: actions/checkout@v3
+      - uses: actions/setup-python@v4
+        with:
+          python-version: '3.10'
+
+      - run: pip install build
+
+      - name: Build sdist
+        run: python -m build --sdist
+
+      - uses: actions/upload-artifact@v2
+        with:
+          name: Sdist
+          path: dist/*.tar.gz
+
 
   # if it's a tag, create a release and attach the artifacts to it
   attach-assets:
@@ -99,6 +157,7 @@ jobs:
     if: ${{ !failure() && !cancelled() && startsWith(github.ref, 'refs/tags/') }}
     needs:
       - build-debs
+      - build-wheels
       - build-sdist
     runs-on: ubuntu-latest
     steps:
diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 16fb4b43e2bda65084c1ba18db1e3306136f1a96..5f96bdfa7f272744d402229d5c2b2090d8748dbd 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -139,6 +139,12 @@ jobs:
     steps:
       - uses: actions/checkout@v2
 
+      - name: Install Rust
+        uses: actions-rs/toolchain@v1
+        with:
+            toolchain: 1.61.0
+            override: true
+
       # There aren't wheels for some of the older deps, so we need to install
       # their build dependencies
       - run: |
@@ -175,7 +181,7 @@ jobs:
           python-version: '3.7'
           extras: "all test"
 
-      - run: poetry run trial -j 2 tests
+      - run: poetry run trial -j2 tests
       - name: Dump logs
         # Logs are most useful when the command fails, always include them.
         if: ${{ always() }}
@@ -247,6 +253,11 @@ jobs:
       - uses: actions/checkout@v2
       - name: Prepare test blacklist
         run: cat sytest-blacklist .ci/worker-blacklist > synapse-blacklist-with-workers
+      - name: Install Rust
+        uses: actions-rs/toolchain@v1
+        with:
+            toolchain: 1.61.0
+            override: true
       - name: Run SyTest
         run: /bootstrap.sh synapse
         working-directory: /src
@@ -353,6 +364,12 @@ jobs:
         with:
           path: synapse
 
+      - name: Install Rust
+        uses: actions-rs/toolchain@v1
+        with:
+            toolchain: 1.61.0
+            override: true
+
       - name: Prepare Complement's Prerequisites
         run: synapse/.ci/scripts/setup_complement_prerequisites.sh
 
diff --git a/.gitignore b/.gitignore
index e58affb24125fee70f85894d7f89a59e3e474bd0..31a60bb7bd3898a4cb5c659b237b314817c74a7c 100644
--- a/.gitignore
+++ b/.gitignore
@@ -60,3 +60,10 @@ book/
 # complement
 /complement-*
 /master.tar.gz
+
+# rust
+/target/
+/synapse/*.so
+
+# Poetry will create a setup.py, which we don't want to include.
+/setup.py
diff --git a/Cargo.toml b/Cargo.toml
new file mode 100644
index 0000000000000000000000000000000000000000..de141bdee9d338e5eb4d0448bb285bf78315c526
--- /dev/null
+++ b/Cargo.toml
@@ -0,0 +1,5 @@
+# We make the whole Synapse folder a workspace so that we can run `cargo`
+# commands from the root (rather than having to cd into rust/).
+
+[workspace]
+members = ["rust"]
diff --git a/build_rust.py b/build_rust.py
new file mode 100644
index 0000000000000000000000000000000000000000..5c5e557ee847589d9a90c10878c876c6014aef63
--- /dev/null
+++ b/build_rust.py
@@ -0,0 +1,20 @@
+# A build script for poetry that adds the rust extension.
+
+import os
+from typing import Any, Dict
+
+from setuptools_rust import Binding, RustExtension
+
+
+def build(setup_kwargs: Dict[str, Any]) -> None:
+    original_project_dir = os.path.dirname(os.path.realpath(__file__))
+    cargo_toml_path = os.path.join(original_project_dir, "rust", "Cargo.toml")
+
+    extension = RustExtension(
+        target="synapse.synapse_rust",
+        path=cargo_toml_path,
+        binding=Binding.PyO3,
+        py_limited_api=True,
+    )
+    setup_kwargs.setdefault("rust_extensions", []).append(extension)
+    setup_kwargs["zip_safe"] = False
diff --git a/changelog.d/12595.misc b/changelog.d/12595.misc
new file mode 100644
index 0000000000000000000000000000000000000000..2e0dd68a0f942b2c810afbe3f6888bb3553cac5e
--- /dev/null
+++ b/changelog.d/12595.misc
@@ -0,0 +1 @@
+Add a stub Rust crate.
diff --git a/debian/build_virtualenv b/debian/build_virtualenv
index ed916ac97a4a9eaa476f54ce0c5692732e749100..dd97e888ba761f1f398fd66a2c6491ccc6061c1b 100755
--- a/debian/build_virtualenv
+++ b/debian/build_virtualenv
@@ -61,7 +61,7 @@ dh_virtualenv \
     --extras="all,systemd,test" \
     --requirements="exported_requirements.txt"
 
-PACKAGE_BUILD_DIR="debian/matrix-synapse-py3"
+PACKAGE_BUILD_DIR="$(pwd)/debian/matrix-synapse-py3"
 VIRTUALENV_DIR="${PACKAGE_BUILD_DIR}${DH_VIRTUALENV_INSTALL_ROOT}/matrix-synapse"
 TARGET_PYTHON="${VIRTUALENV_DIR}/bin/python"
 
@@ -78,9 +78,14 @@ case "$DEB_BUILD_OPTIONS" in
 
         cp -r tests "$tmpdir"
 
+        # To avoid pulling in the unbuilt Synapse in the local directory
+        pushd /
+
         PYTHONPATH="$tmpdir" \
             "${TARGET_PYTHON}" -m twisted.trial --reporter=text -j2 tests
 
+        popd
+
         ;;
 esac
 
diff --git a/debian/changelog b/debian/changelog
index 2b7b329b6b3eb9409711d466cb4c9693cee34e49..bd2d56e738fa463a3becc188a26e35b686f5dc2e 100644
--- a/debian/changelog
+++ b/debian/changelog
@@ -12,11 +12,15 @@ matrix-synapse-py3 (1.66.0) stable; urgency=medium
 
 matrix-synapse-py3 (1.66.0~rc2+nmu1) UNRELEASED; urgency=medium
 
+  [ Jörg Behrmann ]
   * Update debhelper to compatibility level 12.
   * Drop the preinst script stopping synapse.
   * Allocate a group for the system user.
   * Change dpkg-statoverride to --force-statoverride-add.
 
+  [ Erik Johnston ]
+  * Disable `dh_auto_configure` as it broke during Rust build.
+
  -- Jörg Behrmann <behrmann@physik.fu-berlin.de>  Tue, 23 Aug 2022 17:17:00 +0100
 
 matrix-synapse-py3 (1.66.0~rc2) stable; urgency=medium
diff --git a/debian/rules b/debian/rules
index 3b79d560744f431d6c719dfef857f2ede1e59204..914d068f2abde250dfd3a2d1c145754c73b06ad6 100755
--- a/debian/rules
+++ b/debian/rules
@@ -12,6 +12,8 @@ override_dh_installsystemd:
 # we don't really want to strip the symbols from our object files.
 override_dh_strip:
 
+override_dh_auto_configure:
+
 # many libraries pulled from PyPI have allocatable sections after
 # non-allocatable ones on which dwz errors out. For those without the issue the
 # gains are only marginal
diff --git a/docker/Dockerfile b/docker/Dockerfile
index b87d263cff53743efd5e8326cd3063ecfc1f77e7..a057bf397b186ce0c39ad76cada3becf2b282ddc 100644
--- a/docker/Dockerfile
+++ b/docker/Dockerfile
@@ -92,11 +92,20 @@ RUN \
     libxml++2.6-dev \
     libxslt1-dev \
     openssl \
-    rustc \
     zlib1g-dev \
     git \
+    curl \
     && rm -rf /var/lib/apt/lists/*
 
+
+# Install rust and ensure its in the PATH
+ENV RUSTUP_HOME=/rust
+ENV CARGO_HOME=/cargo
+ENV PATH=/cargo/bin:/rust/bin:$PATH
+RUN mkdir /rust /cargo
+
+RUN curl -sSf https://sh.rustup.rs | sh -s -- -y --no-modify-path --default-toolchain stable
+
 # To speed up rebuilds, install all of the dependencies before we copy over
 # the whole synapse project, so that this layer in the Docker cache can be
 # used while you develop on the source
@@ -108,8 +117,9 @@ RUN --mount=type=cache,target=/root/.cache/pip \
 
 # Copy over the rest of the synapse source code.
 COPY synapse /synapse/synapse/
+COPY rust /synapse/rust/
 # ... and what we need to `pip install`.
-COPY pyproject.toml README.rst /synapse/
+COPY pyproject.toml README.rst build_rust.py /synapse/
 
 # Repeat of earlier build argument declaration, as this is a new build stage.
 ARG TEST_ONLY_IGNORE_POETRY_LOCKFILE
diff --git a/docker/Dockerfile-dhvirtualenv b/docker/Dockerfile-dhvirtualenv
index fbc1d2346fb8ed9a991161c053ff58f571ee11d5..ca3a259081c34d97fd32a8b39b888bfdf3387895 100644
--- a/docker/Dockerfile-dhvirtualenv
+++ b/docker/Dockerfile-dhvirtualenv
@@ -72,6 +72,7 @@ RUN apt-get update -qq -o Acquire::Languages=none \
     && env DEBIAN_FRONTEND=noninteractive apt-get install \
         -yqq --no-install-recommends -o Dpkg::Options::=--force-unsafe-io \
         build-essential \
+        curl \
         debhelper \
         devscripts \
         libsystemd-dev \
@@ -85,6 +86,15 @@ RUN apt-get update -qq -o Acquire::Languages=none \
         libpq-dev \
         xmlsec1
 
+# Install rust and ensure it's in the PATH
+ENV RUSTUP_HOME=/rust
+ENV CARGO_HOME=/cargo
+ENV PATH=/cargo/bin:/rust/bin:$PATH
+RUN mkdir /rust /cargo
+
+RUN curl -sSf https://sh.rustup.rs | sh -s -- -y --no-modify-path --default-toolchain stable
+
+
 COPY --from=builder /dh-virtualenv_1.2.2-1_all.deb /
 
 # install dhvirtualenv. Update the apt cache again first, in case we got a
diff --git a/docs/deprecation_policy.md b/docs/deprecation_policy.md
index 359dac07c3dca6d7bfcf9a902bad3f13d8d24b6e..b8a46e3d60e135676dbb6f61608fd1c5ed036c20 100644
--- a/docs/deprecation_policy.md
+++ b/docs/deprecation_policy.md
@@ -18,6 +18,12 @@ documented at [https://endoflife.date/python](https://endoflife.date/python) and
 [https://endoflife.date/postgresql](https://endoflife.date/postgresql).
 
 
+A Rust compiler is required to build Synapse from source. For any given release
+the minimum required version may be bumped up to a recent Rust version, and so
+people building from source should ensure they can fetch recent versions of Rust
+(e.g. by using [rustup](https://rustup.rs/)).
+
+
 Context
 -------
 
@@ -31,3 +37,10 @@ long process.
 By following the upstream support life cycles Synapse can ensure that its
 dependencies continue to get security patches, while not requiring system admins
 to constantly update their platform dependencies to the latest versions.
+
+For Rust, the situation is a bit different given that a) the Rust foundation
+does not generally support older Rust versions, and b) the library ecosystem
+generally bump their minimum support Rust versions frequently. In general, the
+Synapse team will try to avoid updating the dependency on Rust to the absolute
+latest version, but introducing a formal policy is hard given the constraints of
+the ecosystem.
diff --git a/docs/development/contributing_guide.md b/docs/development/contributing_guide.md
index 4e1df5116453117feeb761ac8b1cedac25d6884d..cb0d727efa639c42e55e7b4219a476f7d77559c9 100644
--- a/docs/development/contributing_guide.md
+++ b/docs/development/contributing_guide.md
@@ -28,6 +28,9 @@ The source code of Synapse is hosted on GitHub. You will also need [a recent ver
 
 For some tests, you will need [a recent version of Docker](https://docs.docker.com/get-docker/).
 
+A recent version of the Rust compiler is needed to build the native modules. The
+easiest way of installing the latest version is to use [rustup](https://rustup.rs/).
+
 
 # 3. Get the source.
 
@@ -114,6 +117,11 @@ Some documentation also exists in [Synapse's GitHub
 Wiki](https://github.com/matrix-org/synapse/wiki), although this is primarily
 contributed to by community authors.
 
+When changes are made to any Rust code then you must call either `poetry install`
+or `maturin develop` (if installed) to rebuild the Rust code. Using [`maturin`](https://github.com/PyO3/maturin)
+is quicker than `poetry install`, so is recommended when making frequent
+changes to the Rust code.
+
 
 # 8. Test, test, test!
 <a name="test-test-test"></a>
@@ -195,7 +203,7 @@ The database file can then be inspected with:
 sqlite3 _trial_temp/test.db
 ```
 
-Note that the database file is cleared at the beginning of each test run. Thus it 
+Note that the database file is cleared at the beginning of each test run. Thus it
 will always only contain the data generated by the *last run test*. Though generally
 when debugging, one is only running a single test anyway.
 
diff --git a/docs/setup/installation.md b/docs/setup/installation.md
index bb78b3267aae78fba269cfca3646e49e9d05359d..90737520ba3c8bdc348082dabb63bf45dd2c2627 100644
--- a/docs/setup/installation.md
+++ b/docs/setup/installation.md
@@ -196,6 +196,10 @@ System requirements:
 - Python 3.7 or later, up to Python 3.10.
 - At least 1GB of free RAM if you want to join large public rooms like #matrix:matrix.org
 
+If building on an uncommon architecture for which pre-built wheels are
+unavailable, you will need to have a recent Rust compiler installed. The easiest
+way of installing the latest version is to use [rustup](https://rustup.rs/).
+
 To install the Synapse homeserver run:
 
 ```sh
diff --git a/mypy.ini b/mypy.ini
index e2034e411fa5aabc4b07cf7b34391a15322e268a..64f9097206d1f8cab064635abfd077f3cf4477a1 100644
--- a/mypy.ini
+++ b/mypy.ini
@@ -16,7 +16,8 @@ files =
   docker/,
   scripts-dev/,
   synapse/,
-  tests/
+  tests/,
+  build_rust.py
 
 # Note: Better exclusion syntax coming in mypy > 0.910
 # https://github.com/python/mypy/pull/11329
@@ -181,3 +182,6 @@ ignore_missing_imports = True
 
 [mypy-incremental.*]
 ignore_missing_imports = True
+
+[mypy-setuptools_rust.*]
+ignore_missing_imports = True
diff --git a/poetry.lock b/poetry.lock
index 44df7d395c32bcab16eb70a93f52bf040a2d8b88..cdc69f8ea9da13d466a227040322a0a3eaa49bb6 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1035,6 +1035,18 @@ python-versions = ">=3.6"
 cryptography = ">=2.0"
 jeepney = ">=0.6"
 
+[[package]]
+name = "semantic-version"
+version = "2.10.0"
+description = "A library implementing the 'SemVer' scheme."
+category = "main"
+optional = false
+python-versions = ">=2.7"
+
+[package.extras]
+dev = ["Django (>=1.11)", "check-manifest", "colorama (<=0.4.1)", "coverage", "flake8", "nose2", "readme-renderer (<25.0)", "tox", "wheel", "zest.releaser[recommended]"]
+doc = ["Sphinx", "sphinx-rtd-theme"]
+
 [[package]]
 name = "sentry-sdk"
 version = "1.5.11"
@@ -1099,6 +1111,19 @@ docs = ["furo", "jaraco.packaging (>=9)", "jaraco.tidelift (>=1.4)", "pygments-g
 testing = ["build[virtualenv]", "filelock (>=3.4.0)", "flake8 (<5)", "flake8-2020", "ini2toml[lite] (>=0.9)", "jaraco.envs (>=2.2)", "jaraco.path (>=3.2.0)", "mock", "pip (>=19.1)", "pip-run (>=8.8)", "pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=1.3)", "pytest-flake8", "pytest-mypy (>=0.9.1)", "pytest-perf", "pytest-xdist", "tomli-w (>=1.0.0)", "virtualenv (>=13.0.0)", "wheel"]
 testing-integration = ["build[virtualenv]", "filelock (>=3.4.0)", "jaraco.envs (>=2.2)", "jaraco.path (>=3.2.0)", "pytest", "pytest-enabler", "pytest-xdist", "tomli", "virtualenv (>=13.0.0)", "wheel"]
 
+[[package]]
+name = "setuptools-rust"
+version = "1.5.1"
+description = "Setuptools Rust extension plugin"
+category = "main"
+optional = false
+python-versions = ">=3.7"
+
+[package.dependencies]
+semantic-version = ">=2.8.2,<3"
+setuptools = ">=62.4"
+typing-extensions = ">=3.7.4.3"
+
 [[package]]
 name = "signedjson"
 version = "1.1.4"
@@ -1600,7 +1625,7 @@ url_preview = ["lxml"]
 [metadata]
 lock-version = "1.1"
 python-versions = "^3.7.1"
-content-hash = "0df36bf75561fef340a7af704ed379b235f07a7d4a231aaccec5e7afb87159ca"
+content-hash = "79cfa09d59f9f8b5ef24318fb860df1915f54328692aa56d04331ecbdd92a8cb"
 
 [metadata.files]
 attrs = [
@@ -2472,6 +2497,10 @@ secretstorage = [
     {file = "SecretStorage-3.3.1-py3-none-any.whl", hash = "sha256:422d82c36172d88d6a0ed5afdec956514b189ddbfb72fefab0c8a1cee4eaf71f"},
     {file = "SecretStorage-3.3.1.tar.gz", hash = "sha256:fd666c51a6bf200643495a04abb261f83229dcb6fd8472ec393df7ffc8b6f195"},
 ]
+semantic-version = [
+    {file = "semantic_version-2.10.0-py2.py3-none-any.whl", hash = "sha256:de78a3b8e0feda74cabc54aab2da702113e33ac9d9eb9d2389bcf1f58b7d9177"},
+    {file = "semantic_version-2.10.0.tar.gz", hash = "sha256:bdabb6d336998cbb378d4b9db3a4b56a1e3235701dc05ea2690d9a997ed5041c"},
+]
 sentry-sdk = [
     {file = "sentry-sdk-1.5.11.tar.gz", hash = "sha256:6c01d9d0b65935fd275adc120194737d1df317dce811e642cbf0394d0d37a007"},
     {file = "sentry_sdk-1.5.11-py2.py3-none-any.whl", hash = "sha256:c17179183cac614e900cbd048dab03f49a48e2820182ec686c25e7ce46f8548f"},
@@ -2484,6 +2513,10 @@ setuptools = [
     {file = "setuptools-65.3.0-py3-none-any.whl", hash = "sha256:2e24e0bec025f035a2e72cdd1961119f557d78ad331bb00ff82efb2ab8da8e82"},
     {file = "setuptools-65.3.0.tar.gz", hash = "sha256:7732871f4f7fa58fb6bdcaeadb0161b2bd046c85905dbaa066bdcbcc81953b57"},
 ]
+setuptools-rust = [
+    {file = "setuptools-rust-1.5.1.tar.gz", hash = "sha256:0e05e456645d59429cb1021370aede73c0760e9360bbfdaaefb5bced530eb9d7"},
+    {file = "setuptools_rust-1.5.1-py3-none-any.whl", hash = "sha256:306b236ff3aa5229180e58292610d0c2c51bb488191122d2fc559ae4caeb7d5e"},
+]
 signedjson = [
     {file = "signedjson-1.1.4-py3-none-any.whl", hash = "sha256:45569ec54241c65d2403fe3faf7169be5322547706a231e884ca2b427f23d228"},
     {file = "signedjson-1.1.4.tar.gz", hash = "sha256:cd91c56af53f169ef032c62e9c4a3292dc158866933318d0592e3462db3d6492"},
diff --git a/pyproject.toml b/pyproject.toml
index 8b2b5060b150b3c1b88bc33731bba803b2d8c29a..7cc9de5bc738384530ee3756ebf160ad33560656 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -52,6 +52,9 @@ include_trailing_comma = true
 combine_as_imports = true
 skip_gitignore = true
 
+[tool.maturin]
+manifest-path = "rust/Cargo.toml"
+
 [tool.poetry]
 name = "matrix-synapse"
 version = "1.66.0"
@@ -82,8 +85,17 @@ include = [
     { path = "sytest-blacklist", format = "sdist" },
     { path = "tests", format = "sdist" },
     { path = "UPGRADE.rst", format = "sdist" },
+    { path = "Cargo.toml", format = "sdist" },
+    { path = "rust/Cargo.toml", format = "sdist" },
+    { path = "rust/Cargo.lock", format = "sdist" },
+    { path = "rust/src/**", format = "sdist" },
+]
+exclude = [
+    { path = "synapse/*.so", format = "sdist"}
 ]
 
+build = "build_rust.py"
+
 [tool.poetry.scripts]
 synapse_homeserver = "synapse.app.homeserver:main"
 synapse_worker = "synapse.app.generic_worker:main"
@@ -161,6 +173,15 @@ importlib_metadata = { version = ">=1.4", python = "<3.8" }
 # This is the most recent version of Pydantic with available on common distros.
 pydantic = ">=1.7.4"
 
+# This is for building the rust components during "poetry install", which
+# currently ignores the `build-system.requires` directive (c.f.
+# https://github.com/python-poetry/poetry/issues/6154). Both `pip install` and
+# `poetry build` do the right thing without this explicit dependency.
+#
+# This isn't really a dev-dependency, as `poetry install --no-dev` will fail,
+# but the alternative is to add it to the main list of deps where it isn't
+# needed.
+setuptools_rust = ">=1.3"
 
 
 # Optional Dependencies
@@ -285,5 +306,21 @@ twine = "*"
 towncrier = ">=18.6.0rc1"
 
 [build-system]
-requires = ["poetry-core>=1.0.0"]
+requires = ["poetry-core>=1.0.0", "setuptools_rust>=1.3"]
 build-backend = "poetry.core.masonry.api"
+
+
+[tool.cibuildwheel]
+# Skip unsupported platforms (by us or by Rust).
+skip = "cp36* *-musllinux_i686"
+
+# We need a rust compiler
+before-all =  "curl https://sh.rustup.rs -sSf | sh -s -- --default-toolchain stable -y"
+environment= { PATH = "$PATH:$HOME/.cargo/bin" }
+
+# For some reason if we don't manually clean the build directory we
+# can end up polluting the next build with a .so that is for the wrong
+# Python version.
+before-build = "rm -rf {project}/build"
+build-frontend = "build"
+test-command = "python -c 'from synapse.synapse_rust import sum_as_string; print(sum_as_string(1, 2))'"
diff --git a/rust/Cargo.toml b/rust/Cargo.toml
new file mode 100644
index 0000000000000000000000000000000000000000..0a9760cafcd1c00f3e093e9d27aff234edef26d5
--- /dev/null
+++ b/rust/Cargo.toml
@@ -0,0 +1,21 @@
+[package]
+# We name the package `synapse` so that things like logging have the right
+# logging target.
+name = "synapse"
+
+# dummy version. See pyproject.toml for the Synapse's version number.
+version = "0.1.0"
+
+edition = "2021"
+rust-version = "1.61.0"
+
+[lib]
+name = "synapse"
+crate-type = ["cdylib"]
+
+[package.metadata.maturin]
+# This is where we tell maturin where to place the built library.
+name = "synapse.synapse_rust"
+
+[dependencies]
+pyo3 = { version = "0.16.5", features = ["extension-module", "macros", "abi3", "abi3-py37"] }
diff --git a/rust/src/lib.rs b/rust/src/lib.rs
new file mode 100644
index 0000000000000000000000000000000000000000..fc4eb39154fc2e4f2307a4478983284af7d9602a
--- /dev/null
+++ b/rust/src/lib.rs
@@ -0,0 +1,15 @@
+use pyo3::prelude::*;
+
+/// Formats the sum of two numbers as string.
+#[pyfunction]
+#[pyo3(text_signature = "(a, b, /)")]
+fn sum_as_string(a: usize, b: usize) -> PyResult<String> {
+    Ok((a + b).to_string())
+}
+
+/// The entry point for defining the Python module.
+#[pymodule]
+fn synapse_rust(_py: Python<'_>, m: &PyModule) -> PyResult<()> {
+    m.add_function(wrap_pyfunction!(sum_as_string, m)?)?;
+    Ok(())
+}
diff --git a/stubs/synapse/__init__.pyi b/stubs/synapse/__init__.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/stubs/synapse/synapse_rust.pyi b/stubs/synapse/synapse_rust.pyi
new file mode 100644
index 0000000000000000000000000000000000000000..5b51ba05d78080737e12fd4383be0c5e2652e0c5
--- /dev/null
+++ b/stubs/synapse/synapse_rust.pyi
@@ -0,0 +1 @@
+def sum_as_string(a: int, b: int) -> str: ...
diff --git a/tests/test_rust.py b/tests/test_rust.py
new file mode 100644
index 0000000000000000000000000000000000000000..55d8b6b28cb4745b3ae6ae4346899096cca50e3e
--- /dev/null
+++ b/tests/test_rust.py
@@ -0,0 +1,11 @@
+from synapse.synapse_rust import sum_as_string
+
+from tests import unittest
+
+
+class RustTestCase(unittest.TestCase):
+    """Basic tests to ensure that we can call into Rust code."""
+
+    def test_basic(self):
+        result = sum_as_string(1, 2)
+        self.assertEqual("3", result)