diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 66a818e..1383209 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -276,6 +276,72 @@ jobs:
           ./run-tests.sh /llvm-mingw
           ./run-lldb-tests.sh /llvm-mingw
 
+  # Run the OpenMP tests with the cross-built i686/x86_64 toolchains from above.
+  # This also forces testing the bundled python executables.
+  test-openmp:
+    # Some tests fail here on the 15.x release branch, but it should pass
+    # with versions from git main. Therefore, only include this in scheduled
+    # builds for now.
+    if: (github.event_name == 'schedule') && (github.repository == 'mstorsjo/llvm-mingw')
+    needs: [linux-cross]
+    runs-on: windows-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - { arch: i686, asmflag: }
+          - { arch: x86_64, asmflag: -m64 }
+    steps:
+      - uses: actions/download-artifact@v3
+        with:
+          name: windows-${{matrix.arch}}-toolchain
+      - name: Unpack toolchain
+        run: |
+          Expand-Archive llvm-mingw-*.zip -DestinationPath .
+          del llvm-mingw-*.zip
+          mv llvm-mingw-* c:\llvm-mingw
+          echo "c:\llvm-mingw\bin" | Out-File -FilePath $Env:GITHUB_PATH -Encoding utf8 -Append
+          echo "c:\llvm-mingw\python\bin" | Out-File -FilePath $Env:GITHUB_PATH -Encoding utf8 -Append
+          echo "PYTHON_EXE=c:/llvm-mingw/python/bin/python3.exe" | Out-File -FilePath $Env:GITHUB_ENV -Encoding utf8 -Append
+      - name: Fetch version
+        if: github.event_name == 'schedule'
+        run: |
+          cat c:\llvm-mingw\versions | Out-File -FilePath $Env:GITHUB_ENV -Encoding utf8 -Append
+      - uses: actions/checkout@v3
+      - name: Checkout llvm-project
+        run: |
+          bash -c "CHECKOUT_ONLY=1 ./build-llvm.sh"
+      - name: Build test executables
+        run: |
+          cd llvm-project
+          mkdir build-tools
+          cd build-tools
+          cmake ../llvm `
+            -G Ninja `
+            -DCMAKE_BUILD_TYPE=Release `
+            -DLLVM_TARGETS_TO_BUILD=X86 `
+            -DCMAKE_C_COMPILER=clang `
+            -DCMAKE_CXX_COMPILER=clang++
+          ninja not FileCheck
+          echo "TOOLS=$PWD\bin" | Out-File -FilePath $Env:GITHUB_ENV -Encoding utf8 -Append
+      - name: Build and test OpenMP
+        run: |
+          cd llvm-project
+          mkdir build-openmp
+          cd build-openmp
+          cmake ../openmp `
+            -G Ninja `
+            -DCMAKE_BUILD_TYPE=Release `
+            -DPython3_EXECUTABLE="$Env:PYTHON_EXE" `
+            -DPYTHON_EXECUTABLE="$Env:PYTHON_EXE" `
+            -DOPENMP_LLVM_TOOLS_DIR="$Env:TOOLS" `
+            -DCMAKE_C_COMPILER=clang `
+            -DCMAKE_CXX_COMPILER=clang++ `
+            -DCMAKE_ASM_MASM_COMPILER=llvm-ml `
+            -DLIBOMP_ASMFLAGS=${{matrix.asmflag}}
+          ninja
+          ninja check-openmp
+
   # Test cross-building ffmpeg for all 4 targeted architectures from linux.
   # This is done only on scheduled builds, with a toolchain with assertions
   # enabled, to catch code generation bugs that might trigger asserts, to