Chromebooks can run Android apps from the Play Store now, and it's ridiculously cool. Well, on one Chromebook, anyway: the ASUS Chromebook Flip. As of Chrome version 53 (currently in the early bird Developer channel) it's the only device that's been updated with the functionality. That's a little odd, since Google promotes plenty of other Chromebook devices via the Google Store, including its own Google-branded Chromebook Pixel machines.
According to this Google support page, the next Chromebooks that will be graced with Android app support are the Chromebook Pixel (last year's updated version) and the Acer Chromebook R11, AKA the C738T. Those two models are specifically called out in text above the larger support list, which names pretty much every notable Chrome OS device on the market at the moment. A previous version of the page explicitly said that those two laptops would get Android apps in a newer developer build, which could indicate that the feature isn't coming to the beta or stable channels of Chrome OS any time soon.
Google's Android app on Chrome support list for "2016/2017" is exhaustive, and includes models from manufactures big and small, from Dell, Toshiba, and Lenovo all the way down to companies I've never heard of. Rest assured, Android apps are coming to a Chromebook near you... it might just take a little while.
- Google Chromebook help