Well,
here is a list of 12 chat scripts written in PHP for hosting yourself. And at
HotScripts.com they seem to have a list of 56 chat scripts. These are the two places I would start looking for scripts, but I haven't checked them out yet.
I couldn't pay $30 per month for something for my site so I would have to host myself.
Getting the chat integrated into threads shouldn't be that hard, depending on how the chat script is written. I've integrated threads with my own poll system as well as partly with my own CMS and it has been quite easy.