Gonna try to get this running on my chromebook with crouton using the following documentation:
Update #1: You will first need to install the following package to use the add repo command per the documentation.
apt-get install python-software-properties
Update #2: The final command has changed. The following gist fork provides the updated final command.
sudo apt-get install sublime-text
note the lack of -2 at the end of the command. Also... it works! Yay!