According to a tech I spoke to: The door chime is located in the Body Control Module, just below and in front of the glove box. You can remove this box, and open it up pretty easily. Inside you will see a little transducer, simply unsolder it from the board and away with the chime! Be careful not to bridge anything, or accidenty unsolder anything else. This box controls EVERYTHING pertaining to the accesorys, and even has most of your VATS circuitry in it.
There is a little round circle thing (the transducer-chime) in that black box. It's about 3/4 of an inch. Just pry it off the pc board it's mounted to. Comes off pretty easy. put the module back together plug it back in there are no side effects from this every thing eles works fine.
Or you could either tape or pour some caulk or 'funtak' in and around the transducer. That should muffle it enough to barely hear it.
I haven't tried it yet, but it sounds SHOULD work. HOPE IT HELPS! Good Luck!
The other suggestion was to buy a Kia Sorrento or Hyundai Sante Fe! :)