I don't know if this specific machine will run it or not, because I don't know the exact specs.. just to help give a little perspective to those who gave an emphatic "no" without explanation or elaboration, or said Chromebooks were only web machines, here's a video of an Acer Chromebook running Skyrim on Ubuntu 13.10.
These machines are a lot more capable than the average person realizes.
And take this for what it's worth, because this is just a random video I found when trying to see if this had already been discussed.. but it appears to a guy recording himself playing Skyrim on a Celeron 847: https/www.youtube.com/watch?v=3kcsvQJvbpM
I personally haven't played skyrim on my chromebook as I worry about the heat it will produce and the longevity of my cpu and battery. Maybe in the future this maybe possible as I do know there as some chromebooks out there that have i5 cpus in them.