Well, if you search for Crouton you fill find tutorials to install Ubuntu on a Chromebook. In this page, you will find one for the Chromebook Pixel:

• Create a Boot USB with the Ubuntu version to install with the tool you want (USB Boot Creator from Ubuntu, Linux Live USB Creator for
  Windows...)


• Reboot the ChromeBook by pressing and holding ESC+Refresh and briefly press the power button. It will ask you to reboot into
  Developer Mode.


• When it reboots press “Ctrl+D” Or wait 30 Seconds. Youll see a scary screen about not having a verified OS. Its fine. Just hit
  “Ctrl+D”.


• Once rebooted press “Ctrl+Alt-T” to pull up terminal


• Enter this into terminalchromeos-firmwareupdate --mode=todev crossystem dev_boot_usb=1


• Now your in Developer mode and we can boot from a USB, so Plug your USB drive we made in the last tutorial in, and your USB mouse and
  
  reboot.


• This time when you see the scary screen hit “Ctrl+L” this will pull you into SeaBIOS. When it comes up hit Esc when prompted and select
  
  your USB drive to boot from. It should be 1.


• When Ubuntu boots, make sure your USB mouse is hooked up, and it will ask you if you want try or install it.

From nemesisrobotics.com/installing-linux-on-the-chromebook-pixel/

The minimum system requirements depends of the OS, then, the minimum ones for Ubuntu are these:

Ubuntu Desktop Edition

• 700 MHz processor (about Intel Celeron or better)


• 512 MiB RAM (system memory)


• 5 GB of hard-drive space (or USB stick, memory card or external drive but see LiveCD for an alternative approach)


• VGA capable of 1024x768 screen resolution


• Either a CD/DVD drive or a USB port for the installer media


• Internet access is helpful

From https://help.ubuntu.com/community/Installation/SystemRequirements

And the performance of the OS depends on the hardware support, which you need to check depending of the Chromebook that you have.