Mix 2 tablespoons of the OLD BAY, ketchup, vinegar and molasses in medium bowl until blended. Set aside. Brush chicken with oil. Sprinkle with remaining 1 teaspoon OLD BAY.
Prepare grill for indirect medium-low heat (275°F to 300°F). Preheat grill by turning all burners to medium. Turn off burner(s) on one side. Place chicken on unlit side of grill. Close grill.
Grill 40 to 45 minutes or until internal temperature of thickest part of chicken is 165ºF, turning occasionally. Move chicken to lit side of grill. Brush with barbecue sauce. Turn lit side of grill to high.
Grill, uncovered, 3 to 5 minutes longer or until chicken is charred, turning once and brushing with additional sauce.