Lisa,
You can still gain great upper body strength and muscle definition by using the bands. Do you have anything you can drape them over? My workout room is a renovatated garage, and the overhead garage door is still there for now. I draped the bands over the rod that goes across the garage door. Truthfully, I used this more than I used my powertower. I used the bands over the rod on my powertower sometimes, but I rarely use the tower. My back became very cut using this technique.
Granted this isn't chin ups but you still can get a great workout with the bands. (alot cheaper)
Just a thought. ;-)