Sauté onion and garlic in butter in a heavy saucepan until onion is tender. Combine cranberry sauce, dressing, and sautéed vegetables in a large mixing bowl; stir well.
Place chicken breast halves in a well-greased 13- x 9- x 2-inch baking dish. Pour sauce over chicken. Bake, uncovered, at 400° for 1 hour and 20 minutes or until sauce is bubbly.