The reason for using a chat room in your website is engagement. Chat Room increase engagement in 20%. Sites with chat rooms are making users spend more time in a website, up to 3 times more. Chat Rooms are often added to Forums.
This seems like an interesting idea but to understand what the motivation, one needs to pin point the differences between the two.

Both Chat rooms and forums are methods to communicate with other users over the Internet, but are used in different ways. Chat rooms allow you to communicate with people in real time, forums are more discussions oriented where not all participants have to be online at the same time.

Forums are more organized, with discussions separated into topics called “threads.” Using a chat room in a forum is getting both type of communication and benefits in one place. There are the forum threads where things can be discussed offline and a chat room where real time discussions are being held.

In chat rooms, conversations occur in real time with all the participants logged in and are present. Forums on the other hand tend to be asynchronous, as not all participants are online and posts occur at a much slower pace.

Visitors to a forum can log in a days after a discussion has started and still respond to previous posts.  This is not possible in a chat room discussion, as it take place at a much faster pace. This also means that forums tend to stick to a specific topic, while conversations in chat rooms can rapidly change, depending on the mood of the participants.

Chat Rooms within a forum can help direct the conversation and get faster response to urgent issues. In appose to forum, the chat can be ONLINE only when the moderator is in, to prevent long non relevant discussions and spam.