How to get grub2 to remember last choice?

The documentation in this case is wrong. All variables in /etc/default/grub start with GRUB_, so it's GRUB_DEFAULT=saved, not DEFAULT=saved. I've corrected the Ubuntu wiki to reflect that.

The official grub manual describes this correctly: http://www.gnu.org/software/grub/manual/grub.html#Simple-configuration

Put the following in /etc/default/grub (command line: gedit admin:///etc/default/grub):

GRUB_DEFAULT=saved
GRUB_SAVEDEFAULT=true

Then run:

sudo update-grub

In my case it was not working for entries defined via /etc/grub.d/40_custom which were missing the savedefault line.

menuentry "Chameleon" {
    savedefault ### <<<< this must be added
    set root="(hd1)"
    chainloader +1
}

You are forgetting the number (ie. the "ENTRY is a number or a menu item title." in your text).

sudo grub-set-default 1

for option 1 to be the default.

Always run sudo update-grub after modifying the /etc/default/grub file to apply the changes.