Heat all barbecue sauce ingredients to boiling in 1-quart saucepan, stirring occasionally.
Brush grill rack with vegetable oil. Heat grill to medium heat.
Mix salt, paprika and pepper. Sprinkle both sides of chicken with salt mixture.
Place chicken skin side up on grill rack. Cover and grill 4 to 6 inches from heat 15 minutes; turn chicken. Brush with Barbecue Sauce. Cover and grill 20 to 25 minutes longer, turning and brushing with Barbecue Sauce, until juice of chicken is no longer pink when centers of thickest pieces are cut.