Preheat grill to medium-hot using both burners.
To prepare chicken, loosen skin from breasts by inserting fingers, gently pushing between skin and meat. Combine salt and next 4 ingredients (salt through chile powder); rub under loosened skin.
Turn left burner off (leave right burner on). Coat grill rack with cooking spray. Place chicken on grill rack over right burner; grill 5 minutes on each side or until browned. Move chicken to grill rack over left burner. Cover and cook 35 minutes or until done, turning once. Remove chicken from grill; discard skin.
To prepare sauce, combine mayonnaise and remaining ingredients, stirring with a whisk. Serve with chicken.