1Heat gas or charcoal grill. Using hands, gently loosen skin on chicken, forming pocket between meat and skin. In small bowl, mix remaining ingredients. Spread half of rub under skin on chicken. Spread remaining rub on top, bottom and sides of chicken.
2Carefully brush oil on grill rack. Place chicken, skin sides up, on grill over medium heat. Cover grill; cook 25 minutes, turning once, until juice of chicken is clear when thickest part is cut to bone (165°F).