Do you have to root an Android device to install Ubuntu? Just as the title says. In order to install another ARM based Operating System or to dual boot your phone, do you have to have root access?

I'm currently using a Motorola Atrix, not sure if that matters or not.
Yes. See this method or this one, for example.

As per eldarerathis' comment, these are both for running Ubuntu in a chroot environment.