My Jenkins Continuous Integration Server is on running on a Ubuntu host, configured as follows:
I had a similar problem, and after looking at the main Jenkins System Log I saw the following:
Feb 15, 2013 8:35:44 PM hudson.security.csrf.CrumbFilter doFilter
WARNING: No valid crumb was included in request for /github-webhook/. Returning 403.
The solution is to switch off the CSRF protection - Manage Jenkins > Configure System > Prevent Cross Site Request Forgery exploits. The checkbox is just at the bottom of the first configuration section. After that it all seemed to work happily.