Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x13 inch baking dish.
Arrange chicken breasts in the baking dish. Place one slice of Swiss cheese on top of each chicken breast. Combine cream of chicken soup and milk in a medium bowl, and pour over chicken breasts. Sprinkle with stuffing mix. Pour melted butter over top, and cover with foil.
Bake 50 minutes, or until chicken is no longer pink and juices run clear.
