I figured out how to get Civilization V running on the Acer i3 Chromebook.
First, I put the device into developer mode and installed Linux using Dan Graziano’s instructions posted at CNET (see “How to run both Chrome OS and Ubuntu on a Chromebook“).
Then, from the Ubuntu software center, I installed both PlayOnLinux and the Chromium browser.
PlayOnLinux allows me to play Civ V via the OnLive streaming service. It works just fine, although there’s no sound. (I haven’t messed with the sound drivers yet.) With OnLive, gameplay remains steady through the entire game. In contrast, when run locally, Civ tends to slow down late in the game, as the system takes more time to process moves.
Separately, I downloaded Chromium and installed Steam for Linux. This installs Civ V and all expansion packs locally. This setup supports multi-player mode, which OnLive’s version does not.
Now, to play Civ on my Chromebook, I just hit Ctrl-Alt-T, type shell, then ‘sudo startunity’, and double-click on either the OnLive or Steam icon on the Ubuntu desktop. No need for an old-school PC at all. 🙂