Combine sugar, ketchup, rum, lime juice, butter, ginger, coffee granules and allspice in small saucepan. Bring to a gentle boil; stir until coffee and sugar blend are dissolved. Remove from heat; set aside.
Trim chicken of any visible fat. With sharp knife, make two diagonal slits about 1/2-inch deep on the top side of each breast.
Combine garlic, oil, salt and pepper in small bowl. Rub mixture all over chicken. Arrange chicken slit-side-up on rack in shallow baking pan. Brush chicken with glaze; reserve remaining glaze. Refrigerate for 30 minutes.
Broil chicken for 5 minutes. Turn chicken over; coat with reserved glaze. Broil for an additional 4 to 5 minutes. Turn chicken over again; coat with glaze. Broil for an additional 2 minutes or until tops are sizzling and brown.