Stir the apple, sweet potatoes, onion, nutmeg, cinnamon, ginger, salt, and pepper together in a bowl. Pour into a baking dish and place the chicken breasts on top.
Bake in the preheated oven until the chicken is no longer pink at the bone and the juices run clear, 45 to 60 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).