It's now possible to run MT4 on Chrome OS (mostly: charts are not working yet).
Last year Google released a way to run Android apps on Chrome, so all you have to do is pack the MT4 Android app apk and you're done. I now have MT4 running on my Chromebook!
Just download the APK format file from here (last link on the page). Install ARC Welder (it may download and install the App Runtime for Chrome first, which takes a while, if you don't have any other ARC apps installed first), and use it to pack the MT4 APK. You need to set it to "iphone - portrait", otherwise it won't run.
There's another packager called twerk, but I was not able to make it work. Usually some apps, like MT4 here, will only run with the proper display settings, so you have to play with those settings to see if you are able to find the right ones that will allow it to run. Iphone, portrait are the ones that work with ARC Welder, but for twerk there are more options, and I was not able to find a settings combination that would allow it to run, since there are many more possible combinations.
This should work on Windows, OSX and Linux as well, which will allow the Android app to run there using Chrome.
Only "small" problem right now is that charts are not working, which makes it not very useful, but maybe the MetaQuotes team or somebody else could chip in and try to make it work. Or also, it would be great if they released a full-blown MetaTrader Chrome app.