Chrooted Debian on Android with an X Server installed via F-Droid.

1) If you haven't already, go to www.fdroid.org and download, and install the F-Droid .apk.
2) Select the fdroid icon and download & install Terminal Emulator, Lil' Debi, ConnectBot and X Server.
3) Start the Lil' Debi app and install debian.
4) Once installed and debian is running, start terminal emulator and type:
su
debian
passwd root
(and enter in a new password)
5) Exit terminal emulator when done and start X Server.
7) Press the menu button and click access control.
8) Add the ip address 127.0.0.1 and click apply changes.
9) Press the remote login button and add root@localhost
10) Click on the newly added root@local host option.
11) It should then connect and ask you for a password, which you should type in.
12) Key in:
export DISPLAY=127.0.0.1:0
13) Install an X11 application with:
sudo apt-get install
14) Start the application.
15) Press back twice.

Job done.