I a tried tons of options but still did not succeed in this. if the chat transcript exceeds the lengts of the page, scrolling up or down in the transcript does not result in the the hiding of the addressbar. Probably because the hosting page does not need any scrolling.
Good examples are the webchat-samples. For instance this one. If you start this sample in a mobile browser (I tried Safari on an iphone), the addressbar does not disappear.
I tried all the options in: How to hide a mobile browser's address bar?. With no luck
Any other tricks I could try?