diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 671bf5d6..9b7d5452 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -85,6 +85,8 @@ jobs:
         #       GitHub UI when the workflow run, we avoid using true/false as
         #       values by instead duplicating the name to signal true.
         include:
+          - python: "3.6"
+            oldest_dependencies: oldest_dependencies
           - python: "3.6"
             subdomain: subdomain
           - python: "3.7"
@@ -143,6 +145,14 @@ jobs:
           pip install --upgrade pip
           pip install --upgrade . -r dev-requirements.txt
 
+          if [ "${{ matrix.oldest_dependencies }}" != "" ]; then
+            # take any dependencies in requirements.txt such as tornado>=5.0
+            # and transform them to tornado==5.0 so we can run tests with
+            # the earliest-supported versions
+            cat requirements.txt | grep '>=' | sed -e 's@>=@==@g' > oldest-requirements.txt
+            pip install -r oldest-requirements.txt
+          fi
+
           if [ "${{ matrix.main_dependencies }}" != "" ]; then
               pip install git+https://github.com/ipython/traitlets#egg=traitlets --force
           fi
diff --git a/.gitignore b/.gitignore
index 44a7b3d4..5ff18d83 100644
--- a/.gitignore
+++ b/.gitignore
@@ -28,3 +28,4 @@ htmlcov
 .pytest_cache
 pip-wheel-metadata
 docs/source/reference/metrics.rst
+oldest-requirements.txt