Try building with Python 3.7 in Appveyor.

appveyor.yml

@@ -13,13 +13,13 @@ environment:
     # See: http://www.appveyor.com/docs/installed-software#python
 
     - PYTHON: "C:\\Python27"
-      PYTHON_VERSION: "2.7.x" # currently 2.7.15
+      PYTHON_VERSION: "2.7.x" # currently 2.7.16
       PYTHON_ARCH: "32"
       OPENSSL_LIB: "openssl-1.1.0e-vs2008"
       VS: "Visual Studio 9 2008"
 
     - PYTHON: "C:\\Python27-x64"
-      PYTHON_VERSION: "2.7.x" # currently 2.7.15
+      PYTHON_VERSION: "2.7.x" # currently 2.7.16
       PYTHON_ARCH: "64"
       OPENSSL_LIB: "openssl-1.1.0e-vs2008"
       VS: "Visual Studio 9 2008 Win64"
@@ -49,43 +49,40 @@ environment:
       VS: "Visual Studio 10 2010 Win64"
 
     - PYTHON: "C:\\Python35"
-      PYTHON_VERSION: "3.5.x" # currently 3.5.3
+      PYTHON_VERSION: "3.5.x" # currently 3.5.4
       PYTHON_ARCH: "32"
       OPENSSL_LIB: "openssl-1.1.0e-vs2015"
       VS: "Visual Studio 14 2015"
 
     - PYTHON: "C:\\Python35-x64"
-      PYTHON_VERSION: "3.5.x" # currently 3.5.3
+      PYTHON_VERSION: "3.5.x" # currently 3.5.4
       PYTHON_ARCH: "64"
       OPENSSL_LIB: "openssl-1.1.0e-vs2015"
       VS: "Visual Studio 14 2015 Win64"
 
     - PYTHON: "C:\\Python36"
-      PYTHON_VERSION: "3.6.x" # currently 3.6.6
+      PYTHON_VERSION: "3.6.x" # currently 3.6.8
       PYTHON_ARCH: "32"
       OPENSSL_LIB: "openssl-1.1.0e-vs2015"
       VS: "Visual Studio 14 2015"
 
     - PYTHON: "C:\\Python36-x64"
-      PYTHON_VERSION: "3.6.x" # currently 3.6.6
+      PYTHON_VERSION: "3.6.x" # currently 3.6.8
       PYTHON_ARCH: "64"
       OPENSSL_LIB: "openssl-1.1.0e-vs2015"
       VS: "Visual Studio 14 2015 Win64"
 
-    # Do not build with Python 3.7 until the fix for this issue is published:
-    # https://bugs.python.org/issue34251
-    #
-    #- PYTHON: "C:\\Python37"
-    #  PYTHON_VERSION: "3.7.x" # currently 3.7.0
-    #  PYTHON_ARCH: "32"
-    #  OPENSSL_LIB: "openssl-1.1.0e-vs2015"
-    #  VS: "Visual Studio 14 2015"
-
-    #- PYTHON: "C:\\Python37-x64"
-    #  PYTHON_VERSION: "3.7.x" # currently 3.7.0
-    #  PYTHON_ARCH: "64"
-    #  OPENSSL_LIB: "openssl-1.1.0e-vs2015"
-    #  VS: "Visual Studio 14 2015 Win64"
+    - PYTHON: "C:\\Python37"
+      PYTHON_VERSION: "3.7.x" # currently 3.7.0
+      PYTHON_ARCH: "32"
+      OPENSSL_LIB: "openssl-1.1.0e-vs2015"
+      VS: "Visual Studio 14 2015"
+
+    - PYTHON: "C:\\Python37-x64"
+      PYTHON_VERSION: "3.7.x" # currently 3.7.0
+      PYTHON_ARCH: "64"
+      OPENSSL_LIB: "openssl-1.1.0e-vs2015"
+      VS: "Visual Studio 14 2015 Win64"
 
 install:
   # If there is a newer build queued for the same PR, cancel this one.