You mentioned finding the chicken dead at the edge of your property. I'm guessing the dog is killing them and taking them away where he thinks you all won't find them. It's like house breaking dogs. People who rub their nose in it, or scold the dog for accidents wind up with a urine soaked room or area in the house that is not frequently used thinking their owner won't find it. He knows killing the chicken will have consequences, but he can't resist his natural urges. Only way to prevent it is not giving him the opportunity, which you are now doing keeping him kenneled up. My DH and I used to have a similar problem, where he thought I was just paranoid. But then one day, the neighbor's dog broke into our yard and killed 1/2 my birds. He had to put a few out of their misery for me and had to helped me clean up carcasses and feathers. After that experience, he started taking my word for it. Most of the time he does, but he still challenges me sometimes. Good luck, hope you get to the bottom of it and don't have any more mishaps. It's heart breaking!