It would be nice if you could run UE4 on Chrome OS. Chromebooks are really taking off in the education market and are making inroads in the general consumer market as well.
Ideally, I think the optimal solution would be to target Native Client [NaCl / PNaCl] (https://developer.chrome.com/native-client) just like other UE4 target’s other operating systems.
Supporting a new platform is quite a laborious process, so in the interim I propose adding support for Google’s App Runtime for Chrome (https://developer.chrome.com/apps/getstarted_arc). This will allow developers to run their UE4 Android apps on Chrome OS. ARC isn’t just for Java apps, VLC a native-heavy app will be coming out for Chrome OS soon thanks to ARC (http://www.anandtech.com/show/9082/the-chromebook-pixel-2015-review/5). ARC is rolling out to the stable channel of Chrome OS in April (http://www.slashgear.com/chrome-os-blurs-lines-as-android-app-porting-opens-to-all-31376150/).