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Place the butter into a roasting pan, and melt in the oven. When butter is melted, swirl to coat the bottom of the roasting pan, and place the chicken drumsticks and thighs, potatoes, and unpeeled garlic cloves into the pan. Sprinkle with salt and black pepper; turn the chicken, potatoes, and garlic to coat with butter.
Bake in the preheated oven until the chicken is no longer pink inside and the juices run clear, about 40 minutes, basting 3 times with pan drippings. Brush maple syrup over the chicken pieces, and spoon pan drippings over the potatoes.