Without using a browser plugin/extension like flash or java applet, browser is essentially a one way communication tool. The request has to be initiated by the browser to fetch data. You cannot 'push' data to the browser.
Many web app using Ajax polling method to simulate a server 'push'. The trick is to balance the frequency/data size with the bandwidth and server resources.
I just did a simple observation for gmail. It does a HttpPost polling every 5 seconds. If there's no 'state' change, the response data size is only a few bytes (not including the http headers). Of course google have huge server resources and bandwidth, that's why I mention: finding a good balance.
That is "Improving user experience vs Server resource". You might need to come out with a creative way of polling strategy, instead of a straightforward polling every x seconds.
E.g. If no activity from party A, poll every 3 seconds. While party A is typing, poll every 5 seconds. This is just a illustraton, you can play around with the numbers, or come out with a more efficient one.
Lastly, the data exchange. The challenge is to find a way to pass minimum data sizes to convey the same info.
my 2 cents :)