Now there's an app for Chrome and Chrome OS that lets you run Android apps. It's called ARC Welder (ARC = App Runtime for Chrome, Weld = to unite) and it's mostly for Android developers that want to test their apps before submitting them to Chrome Web Store. You can select any APK file, but not all of them work, especially if they use Google Play Services APIs.
I've tried various APK files from APKMirror.com. A few of them worked properly (IMDb, BBC News, Wikipedia), while others crashed (for example: Amazon and Yahoo Weather), required Google Play Services (like YouTube and other Google apps) or didn't work that well (like Aviary). ARC is still in beta, so there are still many bugs that need to be fixed.