If your Chromebook has an SSD, you're probably less in danger of damaging it on the ride than you could be. The big danger for modern laptops is vibrational damage to the spinning disk drive (conventional hard drive). SSDs are relatively immune from this vibrational damage.

I'd look for a vertical cloth pannier; the cloth shell would add a certain amount of additional protection.

Many of these would work: http://www.rei.com/c/panniers
Larger pannier bags would allow you to stuff a moderately-sized backpack inside without issue; or, put the backpack on one side of a paired set and the laptop on the other.