Index: subversion/libsvn_ra_serf/options.c
===================================================================
--- subversion/libsvn_ra_serf/options.c	(revision 1846667)
+++ subversion/libsvn_ra_serf/options.c	(working copy)
@@ -74,6 +74,10 @@
   /* Have we received any DAV headers at all? */
   svn_boolean_t received_dav_header;
 
+  /* ### FIXME: SVN-4789
+     Have we received the bespoke GitHub request ID header? */
+  svn_boolean_t received_github_request_id_header;
+
   const char *activity_collection;
   svn_revnum_t youngest_rev;
 
@@ -355,6 +359,22 @@
         }
     }
 
+  /* ### FIXME: SVN-4789
+     GitHub's Subversion bridge does not set any DAV: headers in its
+     response, even though it supports bits of our HTTP protocol and
+     returns a valid response body to an OPTIONS request. We try to work
+     around that monumental brokenness by checking for this
+     GitHub-specific response header.
+
+     Note that the case-sensitive string comparison here is intentional;
+     we do *not* want to support any number of strange hacks, so if
+     GitHub changes the case of their header name, this becomes their
+     problem entirely. */
+  else if (strcmp(key, "X-GitHub-Request-Id") == 0)
+    {
+      opt_ctx->received_github_request_id_header = TRUE;
+    }
+
   return 0;
 }
 
@@ -401,8 +421,19 @@
       serf_bucket_headers_do(hdrs, capabilities_headers_iterator_callback,
                              opt_ctx);
 
-      /* Bail out early if we're not talking to a DAV server.
-         Note that this check is only valid if we've received a success
+
+      /* ### FIXME: SVN-4789
+         Treat GitHub as a DAV server, even though it's broken. */
+      if (opt_ctx->received_github_request_id_header
+          && !opt_ctx->received_dav_header)
+        {
+          /* FIXME: We really should emit a warning here, but apparently
+             we don't have a notification API for that. */
+          opt_ctx->received_dav_header = TRUE;
+        }
+
+      /* Bail out early if we're not talking to a DAV server. Note
+         that this check is only valid if we've received a success
          response; redirects and errors don't count. */
       if (opt_ctx->handler->sline.code >= 200
           && opt_ctx->handler->sline.code < 300
@@ -410,7 +441,7 @@
         {
           return svn_error_createf
             (SVN_ERR_RA_DAV_OPTIONS_REQ_FAILED, NULL,
-             _("The server at '%s' does not support the HTTP/DAV protocol"),
+             _("The server at '%s' does not support the WebDAV protocol"),
              session->session_url_str);
         }
 
Index: subversion/tests/cmdline/dav_tests.py
===================================================================
--- subversion/tests/cmdline/dav_tests.py	(revision 1846667)
+++ subversion/tests/cmdline/dav_tests.py	(working copy)
@@ -69,12 +69,15 @@
 
 #----------------------------------------------------------------------
 
-@XFail()
+@Issue(4789)
 @SkipUnless(svntest.main.is_remote_http_connection_allowed)
 def connect_to_github_server(sbox):
   "connect to GitHub's SVN bridge"
 
-  github_mirror_url = 'https://github.com/apache/subversion/trunk'
+  # FIXME: For some reason, trying this against Subversion's own mirror
+  #        always results in: 504 Gateway Timeout.
+  #github_mirror_url = 'https://github.com/apache/subversion/trunk/'
+  github_mirror_url = 'https://github.com/apache/httpd/trunk/'
 
   # Skip this test if we can't connect to the GitHub server.
   # We check this here instead of in a SkipUnless() predicate decorator,