Although not your exact requirement, the Wowza chat tutorial get you headed in the right direction: http://www.wowza.com/forums/content.php?42.
The wowza link describes an example chat client at /examples/VideoChat/FlashRTMPPlayer/player.html. In order to develop your own chat client you'll need to create your own Flash client, typically using ActionScript. If you aren't a flash developer you could look at OpenTok as an alternative to Wowza. They have a javascript API, no flash development skills required.