One can't really install a full Linux distribution in place of Chrome OS. The ChromeOS firmware (BIOS) restricts the user to using the Linux kernel that is part of Chrome OS.
It is possible to run some Linux distros on top of Chrome OS. Ubuntu, for example, can be run in a chroot environment using something called Crouton. You can read about it at this link:
If it was me, I would use a Chromebook with the ChromeOS it came with. Everyday Google announces more features and apps that can be used with ChromeOS, so, have a good look at the app store and see if it suits your needs.