Preheat oven to 350 F.
Bring a large pot of water to a boil. Add chicken and boil until cooked through, about 15-20 minutes.
Remove chicken from water and dice or shred.
In a large saucepan, heat together the chicken soup, mushroom soup, milk, butter and chicken broth.
Prepare the box stuffing according to package directions (use water from boiled chicken).
Grease a 9-by-13-inch baking dish. Layer in half the dressing mixture, top with the chicken and top with the remaining dressing. Pour soup mixture over top.
Bake for 35-45 minutes.
Serve as the main dish along with any side vegetable.