Place chicken pieces in a lightly greased 9x13 inch baking dish. Make sure rib area of breasts is facing up. Cover dish and bake in the preheated oven for 15 to 20 minutes.
Remove cover and flip chicken pieces. Place pineapple (reserve some for garnish) around chicken. Pour rum over all. Cover and bake for another 15 minutes. Garnish with additional pineapple and serve.
