Although Facebook and Google treat each other as counterparts, here is a way to integrate / add Facebook to Gmail account. Google Buzz might not been able to create enough buzz, but you can similarly make a tab for Facebook on your Gmail Account.
Facebook Gmail Integration is an Google Chrome extension which lets you integrate your Gmail account and Facebook. This Google Chrome add-on lets you check Facebook Notifications, other other Facebook activities
This extension will add a Facebook button on the left sidebar just below Google Buzz. This lets you access Facebook just like you were using Google Buzz.
Ganya.amandagmail.com