I have
123FlashChat installed which you can acess when you click the chat link in the navbar on
my forum.
They do offer to install it for you and link it to your vbulletin for an extra fee. I've had no problems so far.
I have it set so guests and members can access the rooms however you can set it just so its members only.
You only pay a one time fee unless you want them to host it for you.