Requires iOS 6
Avaiable now, Message Box (iOS 7)
Set your Facebook Chat Heads free!
The Facebook app has Chat Heads locked down to being in-app only, this'll help fix that! Take them out of the Facebook app and do whatever you'd like!
A manual chat refresh timer is configurable in settings, though keep in mind a shorter delay will decrease battery life.
*Note* It's much easier if you have the Facebook Messenger app either logged-out, or uninstalled. That way you won't get confused with the push notifications.
Source code available on Github
Requires the Facebook app.
Configure options from Settings app.
See larger Screenshots below..