I've talked about chat here in other topics, so I don't really feel like repeating what has been said before when I should be studying right now.
The chat fell apart because of the users. In the end, it was sort of like this:
Any users who were banned for spam or trolling/flaming would complain or act like it is completely unfair (and end up convincing other users to start a movement or petition), making me wrong for banning them.
If a specific user wasn't banned, I wasn't doing my job correctly and I was the reason chat died.
I don't know if this forum can only use certain chat rooms, but I know for certain Chatroll would be a good choice. It has plenty of options, easy to use and install(even I could), moderation is quick and easy(experience), and only costs for the user unless they removed the fee.
I'd rather not deal with any chat services that cost money, I don't have much. Feldo isn't in support of chat because of what happened on MLP or here, so he wouldn't back it.
I don't know if I have permissions to add a chat to the forum, though.