We win! When I went out to do chores today, there was a young mink (probably a year old) in the trap. Given the size of the animal (about 14" long from the tip of her nose to the base of her tail) and the size of the BR hen she dragged out of the coop, it must have been quite a job for her. Now that we have that taken care of, coop security will begin ASAP.
The best part of all this? DH, who was an avid trapper for many years, said it would never work because mink are too smart to be caught that easily. He was thinking that the human smell on the trap would scare it away. My thinking was that it would be used to the smell because we're in and out of the coop every day. Plus I took away its food source - the hen it had been munching on - so it would naturally go back to where it found its last easy meal. My coop smells a little minky now, but that's better than skunk.