diff --git a/.buildkite/scripts/test_old_deps.sh b/.buildkite/scripts/test_old_deps.sh
new file mode 100755
index 0000000000..dfd71b2511
--- /dev/null
+++ b/.buildkite/scripts/test_old_deps.sh
@@ -0,0 +1,18 @@
+#!/bin/bash
+
+# this script is run by buildkite in a plain `xenial` container; it installs the
+# minimal requirements for tox and hands over to the py35-old tox environment.
+
+set -ex
+
+apt-get update
+apt-get install -y python3.5 python3.5-dev python3-pip libxml2-dev libxslt-dev zlib1g-dev
+
+# workaround for https://github.com/jaraco/zipp/issues/40
+python3.5 -m pip install 'setuptools>=34.4.0'
+
+python3.5 -m pip install tox
+
+export LANG="C.UTF-8"
+
+exec tox -e py35-old,combine
diff --git a/changelog.d/6880.misc b/changelog.d/6880.misc
new file mode 100644
index 0000000000..8344a6ed1e
--- /dev/null
+++ b/changelog.d/6880.misc
@@ -0,0 +1 @@
+Fix continuous integration failures with old versions of `pip`, which were introduced by a release of the `zipp` library.