Running Android apps on a Chromebook is possible, although they run but not so well as you would expect. When using these apps on a Chromebook, the app pauses when a user switches away.
This, however, is ok if its on an Android device because most apps pauses when they not on screen so as to save the device battery life. But for an app to pause on a computer with multi window interface is somewhat you don't expect from a computer. Anyway, theres a solution on how to make Android apps more functional on Chromebook.
According to Chrome Unboxed, the Chrome OS 64 beta has an Android Parallel Tasks which lets Android apps work without pausing when a user switches away.
Since this feature is still in a beta state, theres no guarantee that Android parallel Tasks will reach the stable stage of Chrome OS 64. This development is a good one toward the long awaited integration of Android and Chrome OS.