There doesn't seem to be a chromium (or Google Chrome) port available in Ubuntu Touch (OTA10.1, bq M10). Does one exist, or are there any plans to have one (even without touch / small screen optimizations)?
The system browser in the phone/tablet images is based on the Chromium Content API, and so is roughly the same experience as one would have with Chromium.
If you wish to use Chromium as a legacy X11 app, you should be able to install it inside the legacy apps container with Libertine, in the same way that Firefox/Libreoffice are available.
Google does not provide generic ARM builds of Chrome, so the proprietary Chrome browser version will not be usable.
You can use the command line tools to install applications in a libertine container. First you create a container in the writable part of the file system. I used the instructions here
The intsructions also tell you how to make a desktop file so it appears in the apps scope. I successfully installed emacs this way.
If you try to do this in the terminal app, you will run into problems due to lack of permissions. The easiest way around this is to start the ssh server with
sudo android-gadget-service enable ssh
ssh-keygen cat ~/.ssh/id_rsa.pub >> ~/.ssh/authorized_keys eval $(ssh-agent) ssh localhost
Now you can follow the instructions and set up your libertine container and install applications. This script automates the process (I haven't tried it):