Facebook is working on bringing Chat Heads, one of the most liked features of Facebook Home, to the iOS app. The app update has already been pushed out to iOS devices--I just downloaded it moments ago--and the update text says that Chat Heads will be coming to everyone over the "next few weeks."
Of course, the implementation will differ slightly. Chat heads will only show up when being used in the Facebook App. When we reported that iOS might be getting Facebook Home, the details were likely regarding this update that has since been released. Users will also be getting "stickers" in the coming weeks.
The Facebook App is available from the iOS App Store.