Not unless Parachat support it and I don't think they do. I looked previously for a good chat application that I could integrate into the forums but I haven't found one yet. I will look into it again and see what options are available.
As Katie May suggested you could try - You must be logged in to see this link. Choose the green option (its free). You can also choose a free subdomain like leanah.4t.com For support though, you will need to contact whatever free host you choose.