Have a look at how its done in TeamLiquid page(view source) - they use IFrame like this:
<iframe class="videoplayer" src="http://www.twitch.tv/embed?channel=khaldor" height="478" width="800" frameborder="0" scrolling="no"></iframe>
so it might just be as simple as that..
To embed this on a page just put the IFrame wherever you want and change the channel querystring from khaldor to your username on twitch (for your channel).
Chat should be done the same way.