You can run either Linux or Chrome OS on most Chromebooks without any trouble. However, I wouldn’t want to try to run them together on an older Chromebook or an ARM-powered one.

Chrome Remote Desktop. Run apps on systems you control -- or support. Chrome Remote Desktop allows remote access from your Chromebook to a Mac, Windows, or Linux system that also has Chrome installed.

Chromebooks with the right stuff inside now are able to install and run a complete Linux experience with the KDE desktop without giving up the Chrome OS on the same device. It is not yet flawless, but ...