How would I make my scroll bar automatically fix itself to to the bottom of a div?

I am making a web chat application and I am in need of some help. I am appending some paragraphs to a div, and I have set overflow to auto. When the content of the div containing the chat is full, it creates a scroll bar but stays at the top of the div. I would like the scroll to be fixed to the bottom so that users don't need to scroll each time they receive a message. What should I do?