Whisk apple cider, brown sugar, cinnamon, lemon juice, and nutmeg together in a bowl.
Place chicken breasts in a single layer in the bottom of a large casserole dish. Pour apple juice mixture over chicken breasts. Cover casserole dish with aluminum foil.
Bake chicken breasts in the preheated oven until no longer pink in the center and the juices run clear, about 1 hour. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).