All chat web parts share a common property - Group name. This property allows you to have multiple instances of the same web part in one chat implementation, with each of the instances acting on its own.
For example, you can enable chat users to contribute to two chat rooms at the same time.
1. Place the Chat send message web part on a page. Set its Chat room property to an existing room. Set its Group name to Group1.
2. Place the Chat messages web part on the same page. Set its properties as for the previous web part.
3. Add the same pair of web parts once again, but set their Room name property to another existing room and their Group name to Group2.
When you view the page on the live site, you can see that each pair of web parts is tied to a different chat room and you can use them both at the same time.