How do I disable Facebook Chat Heads on the iPhone?
There doesn't seem to be a way to turn off the Facebook Chat Head feature on iOS devices. You can turn off the Chat option, but this does not solve the problem, and it blocks your friends from being able to send you personal messages. The chat head bubbles will also still pop up when you access your Message screen even if you disable the Chat option.
To turn off Chat, swipe left to open the Chat screen, tap the icon at the top right of the display, and select "Turn Of Chat". Remember, this will not put and end to those little annoying heads cluttering up your display.
UPDATE: If you haven’t synched your device to your computer since you updated the Facebook app, you can try to re-install the earlier version to your iPhone by following these instructions.