Chrome uses (a fork of) Webkit if you didn't know, which is also used by Safari. Here's a few questions that are of the same vein:
- Embedding Webkit with C#
- Embedding Gecko (Firefox engine) with C#
The webkit one isn't great as the other answer states, one version no longer works (the google code one) and the Mono one is experimental. It'd be nice if someone made the effort to make a decent .NET wrapper for it but it's not something anyone seems to want to do - which is surprising given it now has support for HTML5 and so many other features that the IE(8) engine lacks.
Update (2014)
There's new dual-licensed project that allows you embed Chrome into your .NET applications called Awesomium. It comes with a .NET api but requires quite a few hacks for rendering (the examples draw the browser window to a buffer, paint the buffer as an image and refresh on a timer).
I think this is the browser used by Origin in Battlefield 3.
Update (2016)
There is now DotnetBrowser, a commercial alternative to Awesomium. It's based off Chromium.
