Currently, Google Chrome can be installed on 32 or 64 bit Ubuntu 8.04 or later, or 32 bit Debian 5. Support for other Linux distributions should come soon.
I tested Chrome on Ubuntu 9.04, and I must say that it really is built for speed. Although not noticeably faster than my current version of Firefox (3.0.10), I'm still impressed. Because at this early stage of development, Chrome has shown that it has what it takes to dominate the browser market.
So how unstable and incomplete is this developer version of Chrome? --At first, I didn't really notice its instability since it didn't crash on me. But upon checking my system stats, I found out that it is still (understandably) resource hungry as it is not efficient in utilizing RAM and CPU.
As noted on The Chromiun Blog, here are some of the things that the current version of Chrome for Linux can't do: play Flash videos; change privacy settings; set default search provider; print; Of course, support for Google Chrome extensions is still missing.
For your eyes only, here are some screenshots of Google Chrome on Linux in action and rendering some of my favorite Linux-related sites:



For me, Chrome will remain as an alternative to Firefox until maybe it gets everything polished, and until some useful plugins are available and are well-supported.
Last time, I was told that chrome is a proprietary fork of chromium, hence we don't have the whole source code. It's not open source software the GPL way.
Am I wrong or not?
(Disclaimer: I'm a Chrome developer,
but not an omniscient one :-)
It's hard to believe that Linux actually made Google possible and made it rich but remain the last OS to get a worthwhile native programme that's written by Google.
Google a very good search engine - actually (still) the best imo but it's not better than Microsoft as a company. Power, control and the mighty dollars.
I will stick to the Fox until Konqueror is as good. I don't have any plans to install Chrome on Linux.
Epiphany... well... does it pull down all gnome when I want to use it. If I can have epiphany with a mere gtk dependency, that would be great! Well... some services are sort of mandatory, for instance the key ring... I wonder if gnome key ring pulls down all gnome too...
Try Midori if you want a fast lightweight GTK web browser running on Webkit.
But having a LGPLed CSS rendering engine is great.