To get Ubuntu running on your Acer C710 Chromebook you have the the choice between running it in a chroot environment next to the running Chrome OS or install it in a new partition and boot directly the Ubuntu kernel. I used the 2. option in the past but had some issues with drivers and updating the system. My recommendation is to use Install option 1.

Recovery

If you want to start fresh or your system does not boot anymore, follow the instructions at https://support.google.com/chromebook/answer/1080595?hl=en to recover your system.

Developer mode

To install Ubuntu, the Chromebook needs to be in developer mode. The download part of the installation may be speed up by using a LAN cable instead of Wi-Fi.

  • Switch off the Chromebook
  • Hold down the ESC and F3 keys and poke the Power button
  • After ca 5s press Ctrl-D and on the appearing screen confirm the switch into developer mode by pressing Return

Install Ubuntu in a chroot to use it parallel to Chrome OS at the same time

  • Download https://goo.gl/fd3zc
  • Press Ctrl+Alt+T to open a shell in the browser and enter the command shell
  • Install crouton, remove -e if you do not want to encrypt the installation
sh ~/Downloads/crouton -e -r trusty -t xiwi,xfce

To get into Ubuntu, run: 

sudo enter-chroot
startxfce4

Alternative Install option: Install Ubuntu on a partition to boot from

  • Boot into Chrome OS, configure the network but do not log in
  • To get to the console mode, press CTRL+ALT+F2
  • Login as user chronos

The modern chrx installer does not support the C710 yet, only C720 and other models. Once the support is added, it might be worth trying out GalliumOS. So for now you have to use the old ChrUbuntu installer to install Ubuntu:

curl -LOs http://goo.gl/s9ryd && sudo bash s9ryd

Enter a size for the Ubuntu partition size and confirm. The Chromebook will now reboot and restore Chrome OS into the new partitioned system.

Repeat the above steps from getting into console step, but this time you can specify a parameter to the execution of the installer script. You can give a specific Ubuntu destribution as parameter (kubuntu-desktop, lubuntu-desktop, xubuntu-desktop, edubuntu-desktop or ubuntu-standard), I recommend using lubuntu-desktop because it uses less RAM than the other ones with a GUI. Execute:

curl -LOs http://goo.gl/s9ryd && sudo bash s9ryd

This will install the latest Ubuntu LTS release. After the installation is done and you reboot, you will be inside Ubuntu. You can login with user user and password user. When the system booted correctly, you can set to boot Ubuntu by default by executing:

sudo cgpt add -i 6 -P 5 -S 1 /dev/sda

If you want to boot into Chrome OS again, execute:

sudo cgpt add -i 6 -P 0 -S 1 /dev/sda