A chin falling on another chin could cause head trauma or other broken bones for sure. Most of the time chins can take that type of impact, but if the chin is in the right place, an impact could slam the head into the floor of the cage or into the side. It is going to be worse if the chin falls from higher up and hits the other chin with more force. I've seen them run into each other about a billion times, but I have mostly one level cages and the chins aren't injured. But, with enough force applied in just the right way a chin could get hurt.