For my understanding, Chrome Book is more than just a browser, so I am wondering, if it is possible to install Android Studio on Chrome Book.
Credit to @navigaid
You can, but you are required to install additional linux flavor on your Chromebook i.e, Crouton project. It allows an easy method of doing that.
remember that ChromeOS runs on Linux, and you are basically adding another Linux flavor to your Chromebook.
Some useful links,
or you may follow this step by step guide on how to use Crouton to Install an Ubuntu Chroot on Chromebook.
source
Yes you can.
As of this writing, PixelBook has already been able to run Linux applications including Android Studio. Hopefully this feature will eventually roll out to other high end Chrome OS devices in the near future.
source: Preview Android Studio on Chromebooks