Install Yahoo Messenger Version 11 (Beta). Then connect your Yahoo account with your FB account.
(Click image to enlarge)
And click the "Sign In" link to see your FB list of friends who are online on FB Chatbox
(Click image to enlarge)
You don't have to open your browser, regardless if you're online or not in your FB Chatbox.
I've done some tests (see image below) using my FB account (left) and my "Other" FB account (right) to chat with each other.
The message was sent across to your friend's FB Chatbox.
(Click image to enlarge)
The downside so far is that the messages can also be seen from your FB page even when you're in Yahoo Messenger. Through this, the conversations can never be private.
(Click image to enlarge)
So don't leave your FB page open at home. Don't let your browser save your passwords. Don't give your password to even your closest friend. Or better, don't use Yahoo Messenger to chat with your FB friends.
Another down side is, since Yahoo and Facebook have their own network infrastructure, the data exchange is not that close as real-time. There are delays. Meaning, you can't be notified immediately while in YM as soon as your FB friend signs out and vice versa. Your messages during this period of delay will have a 50% chance of being sent across but not vice versa. The next time you open your FB page...you'll get this:
(Click image to enlarge)
