diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
new file mode 100644
index 00000000..ad5a2660
--- /dev/null
+++ b/.github/workflows/tests.yml
@@ -0,0 +1,71 @@
+name: Tests
+
+on:
+  push:
+    branches: [ 'master' ]
+  pull_request:
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  complement:
+    runs-on: ubuntu-latest
+    steps:
+      # Env vars are set file a file given by $GITHUB_PATH. We need both Go 1.17 and GOPATH on env to run Complement.
+      # See https://docs.github.com/en/actions/using-workflows/workflow-commands-for-github-actions#adding-a-system-path
+      - name: "Set Go Version"
+        run: |
+          echo "$GOROOT_1_17_X64/bin" >> $GITHUB_PATH
+          echo "~/go/bin" >> $GITHUB_PATH
+
+      - name: "Install Complement Dependencies"
+        # We don't need to install Go because it is included on the Ubuntu 20.04 image:
+        # See https://github.com/actions/virtual-environments/blob/main/images/linux/Ubuntu2004-Readme.md specifically GOROOT_1_17_X64
+        run: |
+          sudo apt-get update && sudo apt-get install -y libolm3 libolm-dev
+          go get -v github.com/haveyoudebuggedit/gotestfmt/v2/cmd/gotestfmt@latest
+
+      - name: Run actions/checkout@v2 for dendrite
+        uses: actions/checkout@v2
+        with:
+          path: dendrite
+
+      # Attempt to check out the same branch of Complement as the PR. If it
+      # doesn't exist, fallback to master.
+      - name: Checkout complement
+        shell: bash
+        run: |
+          mkdir -p complement
+          # Attempt to use the version of complement which best matches the current
+          # build. Depending on whether this is a PR or release, etc. we need to
+          # use different fallbacks.
+          #
+          # 1. First check if there's a similarly named branch (GITHUB_HEAD_REF
+          #    for pull requests, otherwise GITHUB_REF).
+          # 2. Attempt to use the base branch, e.g. when merging into release-vX.Y
+          #    (GITHUB_BASE_REF for pull requests).
+          # 3. Use the default complement branch ("master").
+          for BRANCH_NAME in "$GITHUB_HEAD_REF" "$GITHUB_BASE_REF" "${GITHUB_REF#refs/heads/}" "master"; do
+            # Skip empty branch names and merge commits.
+            if [[ -z "$BRANCH_NAME" || $BRANCH_NAME =~ ^refs/pull/.* ]]; then
+              continue
+            fi
+
+            (wget -O - "https://github.com/matrix-org/complement/archive/$BRANCH_NAME.tar.gz" | tar -xz --strip-components=1 -C complement) && break
+          done
+
+      # Build initial Dendrite image
+      - run: docker build -t complement-dendrite -f build/scripts/Complement.Dockerfile .
+        working-directory: dendrite
+
+      # Run Complement
+      - run: |
+          set -o pipefail &&
+          go test -v -json -tags dendrite_blacklist ./tests/... 2>&1 | gotestfmt
+        shell: bash
+        name: Run Complement Tests
+        env:
+          COMPLEMENT_BASE_IMAGE: complement-dendrite:latest
+        working-directory: complement
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