diff --git a/.github/workflows/packaging.yml b/.github/workflows/packaging.yml
new file mode 100644
index 0000000..d5673c6
--- /dev/null
+++ b/.github/workflows/packaging.yml
@@ -0,0 +1,39 @@
+#
+# Test job to see how packaging looks like.
+#
+
+name: Build distributions
+
+on: [push, pull_request]
+
+jobs:
+  build_wheels:
+    name: Build wheels on ${{ matrix.os }}
+    runs-on: ${{ matrix.os }}
+    strategy:
+      matrix:
+        # macos-13 is an intel runner, macos-14 is apple silicon
+        os: [ubuntu-latest, windows-latest, macos-13, macos-14]
+
+    steps:
+      - uses: actions/checkout@v4
+        with:
+          submodules: "true"
+
+      - uses: actions/setup-python@v5
+        with:
+          python-version: "3.12"
+
+      - run: |
+          python -m pip install -U pip
+          pip install build
+
+      - run: python -m build --wheel -vv
+      - if: matrix.os == "ubuntu-latest"
+        run: python -m build --sdist -vv
+        # We only need a single source distribution
+
+      - uses: actions/upload-artifact@v4
+        with:
+          name: dist-${{ matrix.os }}
+          path: dist