Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Bring a pot of water to a boil and reduce heat to medium-low. Cook chicken breasts in the simmering water until no longer pink inside, 5 to 8 minutes. Remove chicken and cut into bite-sized pieces.
Stir chicken broth and water together in a large measuring cup; mixture should total 2 cups. Mix cream of mushroom soup, cream of chicken soup, and 1 cup of chicken broth mixture in a large bowl; stir in chicken. Spread chicken mixture into bottom of prepared baking pan.
Mix remaining 1 cup of chicken broth mixture, melted margarine, and stuffing mix in a bowl; stir to moisten. Spread stuffing mix over chicken mixture.
Bake in the preheated oven until stuffing is lightly browned and casserole is bubbling, 40 to 45 minutes.