To Make Glaze: In a medium bowl combine the ketchup, pineapple juice, molasses, rum, mustard and garlic. Season with salt and pepper to taste and mix well.
Place chicken pieces in a lightly oiled 9x13 inch baking dish; brush both sides with prepared glaze, using about 1/2 of the glaze. Cover dish and refrigerate to marinate for at least 2 hours or overnight. Also, refrigerate remaining glaze.
Preheat oven to 375 degrees F (190 degrees C).
Lightly brush chicken pieces on one side with some of the reserved glaze and bake uncovered in preheated oven for about 25 minutes. Turn pieces, brush with remaining glaze and bake for another 25 minutes or until chicken is tender.
Preheat oven to broil.
Put chicken under broiler and lightly brown on both sides, about 2 to 3 minutes each side. (Note: Watch chicken carefully, as this 'sugary' glaze burns easily!)