Private Chatting

Is there a way of doing this? i was thinkin that when someone is online you can click the little yellow V button (the one that is in the same box as the date that the post was made) and a box pops up with a chat room linked to the person you wanted to chat to, then on the person's screen who you have requested to chat to will have a box pop up, like the one you get when you get a new pm, and it says who has requested and wether or not you wish to accept it. So anyway would this be possible?