Start testing with Python 3.7

.travis.yml

@@ -1,12 +1,29 @@
 dist: trusty
 language: python
-python:
-    - "2.7"
-    - "3.4"
-    - "3.5"
-    - "3.6"
-    - "pypy"
-    - "pypy3"
+
+# Python 3.7+ needs a newer version of openssl than is available in trusty,
+# so these must run on a newer platform (and since travis doesn't yet have
+# containers for xenial, those must use VMs).
+# YAML magic from https://github.com/travis-ci/travis-ci/issues/9069#issuecomment-401924248
+.mixins:
+- &xenial-mixin
+  dist: xenial
+  sudo: true
+  addons:
+    apt:
+      packages:
+        - libgnutls-dev
+
+jobs:
+  include:
+    - python: "2.7"
+    - python: "3.4"
+    - python: "3.5"
+    - python: "3.6"
+    - python: "pypy"
+    - python: "pypy3"
+    - <<: *xenial-mixin
+      python: "3.7"
 install: "python setup.py install"
 script: "python setup.py test"
 notifications: