I am creating a website where users will be able to chat and send files to one another through a browser. I am using GWT for the UI and hibernate with gilead to connect to a mysql database backend.
What would be the best strategy to use so Users can interact together?
I'd say you are looking for comet/AJAX|Server push/etc. See my previous answer on this matter for some pointers. Basically you are simulating inverting the communication between server and client - it's the server that's initiating the connection here, since it wants to, for example, inform the user that his/her friend just went online, etc.
The implementations of this technique change quite rapidly, so I won't make any definitive recommendations - choose the one that best suits your needs :)