Chromium and Google Chrome are different projects though, one backed by google and the other one, a true community contributed open source project. Chromium is still a work in progress while Google Chrome is already in its beta. Since i have been using both of them for a while, I have to say, Google Chrome is much more stable and functional. And once you start using either of these web browsers, all other alternatives out there will be like from a totally different age.
Download Google Chrome for Linux and follow the instructions.