Programming Mindstorms on a chromebook
Update Dec 2016

There is now an app for chromebooks on the chrome store:

https://chrome.google.com/webstore/detail/lego-mindstorms-education/jhnhfnolmcleankdkhfklakpchnccipg?hl=en-US

I have used it to program EV3 version of the bricks. It connects via bluetooth to the EV3 brick (I don't think USB is even supported).  The bluetooth connection can be buggy at times and I've found myself having to re-pair the brick.  

The chrome app saves programs in a format (.ev3m format) which is not compatible with the Mac/Windows desktop versions of the programming app.   Attempts to load programs written on Mac/Windows (.ev3 format) will not load in the app.  Suffice to say transferring programs between a chromebook and the desktop version of the EV3 programming software is difficult and perhaps not possible. There may be a way to download the program from the chrome app onto the brick and then pull the software using the 'Memory Browser' tool into the desktop version but I haven't had time to look into it.

My chromebook has only 2 GB of RAM and the program sometimes struggles to load so I recommend at least 4 GB of RAM in your chromebook.

There is a pretty good Q/A article here: 

https://education.lego.com/en-us/middle-school/explore/c/ev3-chromebook-faq