Same here. I'm using Chrome on Windows 7. There was another forum post (http://www.gamespot.com/forums/topic/27580275?topic_id=27580275)where FabriceEdoua (http://www.gamespot.com/users/FabriceEdoua/) suggested clearing both the Gamespot and Facebook cookies. This got me a bit further as I now got a prompt to login using my Facebook account. But once I logged in, I received this error:

An error may have occurred as part of the login process. You can close this window and try returning to the application, though it may ask you to login again. This is likely due to a bug in the application.

I can login using Facebook using other browsers, so it looks like an issue confined to Google Chrome.