I teach a course on ArcGIS Desktop, and both of the last two times I taught the course I had a student whose computer was a Chromebook.
I normally tell Mac and Linux users to install virtual machine software (VMWare or Oracle Virtualbox), and then install Windows onto a virtual machine in order to have an environment onto which to install ArcGIS Desktop with a student license.
What options (if any) exist for Chromebook users?
Best Answer
If you have access to some servers somewhere, they can use Remote Desktop to connect to Windows servers. You might not even need a server - if you are not in your office you might be able to log out and give them an account on your office PC, which they can then connect to via Remote Desktop and run Windows programs there. This is all subject to local network settings and policies, licenses etc etc.
But running it on the Chromebook? You could install an Ubuntu chroot environment, and then run Windows in a VM (https://github.com/dnschneid/crouton) but ewwww.