I'm assuming you want the LTS (long term support) version of ubuntu.
There is a tool developed for this. It's called crouton.
Since chromeOS is based on linux you'll be able to switch with a simple keyboard shortcut (if you want you can also make it a more traditional dualboot (you'll want this script if you want to do that) but this is imho better.
First things first: make a backup of all the files you want to save that are not in the cloud (because they WILL be lost).
2) Press and hold the Esc and Refresh keys together, then press the Power button (while still holding the other two keys). This will reboot your Chromebook into Recovery Mode.
3) When you get the yellow screen with the exclamation mark hit ctrl + d (This will bring up a prompt asking if you want to turn on Developer Mode.) Press enter (this will take about 15 to 20 min. You'll get a screen with a red exclamation mark but leave it be until it reboots into chromeOS).
4) Download crouton
5) press ctrl + alt + T and you'll get a terminal (linux uses the same shortcuts)
6) type "shell" (without the quotation marks) to get a ubuntu shell
7) type this command
sudo sh -e ~/Downloads/crouton -t xfce
(if you have a touch screen you'll want to change that to include the touch functions)
sudo sh -e ~/Downloads/crouton -t touch,xfce
if you want the unity desktop then change xfce for unity
if you want another release then run this to give you a list of the recognized releases and which distros they belong to.
sh -e ~/Downloads/crouton -r list
8) Let it run. (when it's done it'll ask you for a new username and password)
9) run this command to start your new environment.
sudo startxfce4
10) Now, you can switch back and forth between Chrome OS and Ubuntu using Ctrl+Alt+Shift+Back and Ctrl+Alt+Shift+Forward (if you're on an ARM-based Chromebook) or Ctrl+Alt+Back and Ctrl+Alt+Forward (If you're on an Intel-based Chromebook). In the latter case, you will also need to press Ctrl+Alt+Refresh after pressing Ctrl+Alt+Forward to bring up the desktop. To exit the Linux desktop, just log out of it like you would on a normal PC—you'll close it completely and go back to Chrome OS (after which you can run sudo startxfce4 again to go back).
if you experience problems the crouton link on the top redirects you to the official crouton page including a troubleshooting page
Best Answer
I have! I decided to go ahead and do it today before waiting on an answer to this question.
I used the top answer to this post: Unable to install Ubuntu on Lenovo Y500.
It's for a Y500 but it applies to the Y410P.