For the Barbecue Sauce, mix all ingredients in small saucepan. Simmer on low heat 10 minutes. Remove from heat. Reserve 1/2 cup barbecue sauce for serving.
Brush chicken pieces lightly with oil. Sprinkle generously with OLD BAY.
Grill chicken over medium heat with lid closed about 40 minutes or until chicken is cooked through, turning occasionally. Brush with barbecue sauce during last 10 minutes of grilling. Serve chicken with reserved barbecue sauce.