If you can live without the bang, you could just add a search engine to Chrome with the text "gh". Then, prepending "gh" to a search would just search Github.
!gh { https://github.com/search&q=$QUERY$ }
!ebay { http://www.ebay.co.uk/sch/i.html?&_nkw=$QUERY$ }
Then all browsers (and other apps) could provide these standard shortcuts in their search functions.Reading the site though, it seems poorly adopted? And also not automated (the user has to actively install SearchProviders? Most users don't bother.)