http://watin.sourceforge.net/
WatiN does exactly that, and I believe they recently added Chrome support
Update 6/22/2011:
Currrently WatiN only works on Firefox 2 and 3, not in Firefiox 4 (and almost certainly not in Firefox 5, which was released today). Also, the time of this answer, Chrome support was supposedly being added, but it looks like that never got fully baked and now is not listed as a suported platform on their home page.
Also worth noting, in my experience WatiN got a lot slower when I upgraded to IE9. I saw this on two different machines, and downgrading to IE8 sped the tests back up on both machines.
I still use WatiN heavily, but now mostly for behavior driven design and functional regression testing, which generally are not browser-specific. Then, manually test in FF and Chrome for all progression testing.
Update 9/22/2015:
Elmue is right, it looks like WatiN is no longer being worked on. We've looking into Selenium for our automated acceptance tests now: http://www.seleniumhq.org
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