Code weavers have put together a proof of concept to demostrate that Chromium, the open source version of Google Chrome, can in fact run on other platforms.
Keep in mind that this is a PoC, and not proven to be stable… also there are no auto updates for this. Read more here.
Darran Boyd 
It seemed perfectly stable to me, but the font rendering was a bit off. I believe it had something to do with UTF encoding issues.