I would very much like a better web browser than the one currently in steam, and I know that I can run it without significant decline in performance. I was wondering if there is a way to change it and if there is also a way to embed a chat client as well. Any suggestions?
Xfire and PlayXpert offer web browsers as part of their in-game overlays. There is also the Rogue in-game browser. Xfire offer a preview video of their web browser. All look to have tabbed browsing and offer more features than Steam's, though it's hard for me to say whether they meet your expectations.
Both Xfire and PlayXpert also ship with chat clients.
Raptr's in-game overlay supports AIM and I believe XChat makes available an addon to that end also. Personally I'd try Raptr first. Any of the web browsers may also support AIM Express, an official browser-based AIM client.
Steam uses a webkit-based browser, the same engine that is behind Chrome and Safari. It was chosen above Trident (IE technology) because of crossplatform compatibility (= it runs mostly unchanged on Mac OS X). At best of my knowledge, this cannot be changed.