Is there an app to chat on Facebook on iOS?
Solution 1:
There are two, both from Facebook. It's available in the Messages section of Facebook app, as well as the standalone Facebook Messenger app. The standalone app uses a denser interface, and would be an improvement if you were going to use this heavily, but the section of the complete app isn't much worse.
Solution 2:
Also you can use IM+ it's a free app. And if you like to spending some money you can use IM+ Pro.