It's possible to use a Chromebook/ChromeOS for programming Arduino. The good news is that you don't need to install any software. Instead you will register and use Codebender.cc which is an online version of the Arduino software. We'll still primarily have examples that use the desktop version because it's a little more powerful and is the latest and greatest but codebender does 95% of what the desktop version does and its free too!
Go through their walkthrough setup procedure and install the Chrome Plugin
When you get to this step, select Arduino UNO
And in the next step, your Serial port:
If you're using Windows or Mac you may still need to install drivers so be sure to do that in case the serial port doesnt appear