diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 1f3d57310..89d35fdc1 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -182,6 +182,9 @@ jobs:
           - windows-latest
         python-version:
           - 2.7
+        include:
+          - os: ubuntu-latest
+            python-version: 3.6
 
     steps:
 
@@ -239,9 +242,14 @@ jobs:
       - name: Display tool versions
         run: python misc/build_helpers/show-tool-versions.py
 
-      - name: Run "tox -e integration"
+      - name: Run "Python 2 integration tests"
+        if: ${{ matrix.python-version == '2.7' }}
         run: tox -e integration
 
+      - name: Run "Python 3 integration tests"
+        if: ${{ matrix.python-version != '2.7' }}
+        run: tox -e integration3
+
       - name: Upload eliot.log in case of failure
         uses: actions/upload-artifact@v1
         if: failure()