I discovered that OpenVPN supports connections through an HTTP proxy server. This makes it possible to establish a VPN from a completely firewalled network where the only external access is through a proxy server1. It takes advantage of the fact that SSL connections are simply tunnelled through the server and aren't interfered with like unencrypted connections.
The server setup is almost identical to a normal configuration, except that the tunnel must use TCP instead of UDP (since the proxy server will establish a TCP connection). Since most proxy servers only allow SSL connections to certain ports, you will also need to change the port number that the server listens on. The best is 443 since that is used for HTTPS, but if the server is also running a web server on port 443, then 563 is probably the next best choice. This port is assigned to NNTPS, and is allowed by the default Squid configuration. The following two lines enable TCP connections and change the port number.
The client configuration is also very similar. It simply needs to enable TCP connections, set the correct port number, and specify the proxy server.
OpenVPN can also authenticate to the proxy server using either Basic or NTLM authentication. To enable this add "
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