In a large skillet that has a cover, melt butter over medium heat. Dust chicken lightly with paprika. Brown chicken on both sides in melted butter. Cover; reduce heat. Cook chicken 30 minutes.
Meanwhile, place cabbage slices on bottom of buttered 13-by-9-inch baking dish. Sprinkle with salt and pepper.
Cover dish with aluminum foil. Bake in a preheated 375° F oven 20 minutes, or until cabbage is almost tender. Remove cabbage from oven; uncover.
Arrange apple and onion over cabbage. Sprinkle with sugar.
Place chicken pieces over top. Cover with foil. Bake an additional 25-30 minutes or until cabbage and chicken are tender. Remove from oven; uncover.
Sprinkle with cheese. Return to oven just until cheese melts, about 5 minutes.
Servings: 4