Firefox 17 added a hidden feature to enable notifications and chat from Facebook right in your browser. Here's how to enable it.
To check out the new feature, make sure you've updated to the latest version of Firefox, then type
about:config into the address bar. Promise Firefox you'll be careful, then search for
social.enabled using the about:config search bar. Double-click the
social.enabled option to set it to True. You should find that you have Facebook notifications for friend requests, messages and other posts in the upper right-hand corner of your browser.
Unfortunately, it also adds a chat sidebar and mini-feed to the side of your browser, making this a deal killer for most people (including myself). It would be nice if we had the option to remove this, because it's pretty intrusive -- although, if you spend a lot of time on Facebook chat, I could see it being handy to chat from any window you want. Hopefully, Firefox will develop this feature a little more and give us some options before it's "officially" introduced.
How to Enable Facebook Integration in Firefox [How-To Geek]