Preheat the oven to 425?F. Coat a roasting pan with cooking spray.
In a medium saucepan, combine the bell peppers, onion, garlic, broth, and water. Bring to a boil over high heat. Reduce the heat to medium, cover, and simmer, stirring occasionally, for 5 minutes, or until the vegetables are tender crisp.
Stir in the tomato sauce, raisins, molasses, vinegar, hot pepper sauce, mustard powder, black pepper, and salt. Bring to a boil over high heat.
Place the chicken pieces in the prepared roasting pan. Spoon the sauce over the chicken, turning to coat.
Bake, turning the pieces and basting occasionally with the sauce, for 30 minutes, or until a thermometer inserted in the thickest portion registers 170?F and the juices run clear.