1Heat gas or charcoal grill. In 1-quart saucepan, heat sauce ingredients over medium heat until boiling, stirring occasionally.
2In small bowl, mix 1 teaspoon salt, 1 teaspoon paprika and 1/4 teaspoon pepper. Sprinkle both sides of chicken with salt mixture.
3Carefully brush grill rack with vegetable oil. Place chicken skin side up on grill over medium heat. Cover grill; cook 15 minutes.
4Turn chicken; brush with barbecue sauce. Cover grill; cook 20 to 25 minutes longer, turning and brushing with sauce, until juice of chicken is clear when thickest piece is cut to bone (170°F for breasts; 180°F for thighs and legs).