GUI method

I remember that one of the first things that I made after I installed a fresh version of Ubuntu 13.04 it was to install Chromium browser . And I installed it from Ubuntu Software Center without to add any ppa repository or to download it from somewhere. Also, I remember that just a few days ago Software Updater announced me that there is a new version of Chromium to update.

So it's sure that Canonical have decided to provide the most recent Chromium versions and you don't need to think anymore what is easier way to install Chromium or how to stay up to date with current Chromium releases. And here is the official Ubuntu package of Chromium browser on Launchpad: https://launchpad.net/ubuntu/+source/chromium-browser.

Proof:

As you can see from above image, you can also to install Unity Webapp extension once with Chromum Browser.

Comand-line method

Open a terminal and run next command:

sudo apt-get install chromium-browser

Proof:

As a note, it seems that Chromium Likely to Replace Firefox As Default Browser in Ubuntu 13.10.

If you are interested somehow by other versions of Chromium browser from Personal Package Archives (PPAs), here is a complete list with all of these (some of them have been abandoned): https://launchpad.net/ubuntu/+ppas?name_filter=chromium-browser. And keep in mind that these PPAs are considered by Canonical unsupported and unsecured.