Layer the deboned chicken meat in a lightly greased 9x13 inch baking dish. Sprinkle stuffing mix over the chicken layer.
In a large bowl mix together the soups, broth and evaporated milk. Stir well. Pour this mixture over the stuffing mix, making sure it gets to the bottom of the baking dish (poke around with a fork to let it saturate into the bottom layer). Bake in the preheated oven for 35 to 45 minutes, until it starts to bubble in the center.