Well, we have this one:
Live Chat
And I actually paid for the premium version for a year, but I don't think it was used that much. And I know that there are a bunch of chat apps that can intergrate with our forum (i.e., usernames and passwords), but that's something I didn't do last time because of time restrictions.
I'd consider buying the premium version again if I knew that people would use it.
Do you know what system the other site you mentioned is using? Or can you just post a link to their chat app?