I would think it would be possible to link them to their forum logins. Once a user is logged into the forum, store the fact that the user is logged in using a cookie or session variable, so when the user navigates to the chat page the scripting checks the session variable/cookie and if the user is logged in, bypasses the login screen and goes to the chat.
For a user with no account, create a form for the user's information (login name they wish to use, password, anything else you might want). Upon submittal of the form, the information gets inserted into a database table. Have a field called, for example, "activated" that gets set initially to False/0. If a user tries to login and this field is False/0, then they get an error message saying something like "The site administrator has not yet activated your account". This way they cannot login until you update that field with True/1. You could have some sort of admin form that displays any non-activated accounts where you can check to active them, and at the same time send an email to the user letting them know their account has been activated.