Place chicken breasts in single layer in ungreased 9 x 12 baking pan.
Cover chicken with slices of Swiss cheese. Spread cream of chicken soup over Swiss cheese (more than 1 can may be used if more sauce is desired). Cover soup with a layer of dry stuffing mix. Dot with butter.
Bake at 350 degrees F for 35 to 45 minutes, depending on the thickness of the chicken breasts.