Place chicken, breast side down, on cutting board. With kitchen scissors (or sharp knife), cut along one side of backbone from neck to tail, then cut along other side of backbone and remove bone.
Turn chicken breast side up, and place flat with legs and wings to the sides. Press down on breast bone with palm of hand to flatten chicken.
In large resealable food-storage plastic bag, mix remaining ingredients. Place chicken, breast side down, in bag; seal bag and turn to coat. Refrigerate 8 hours or overnight to marinate, turning once or twice.
Heat gas or charcoal grill on high heat at least 15 minutes before adding chicken.
Remove chicken from marinade; discard marinade. Reduce grill heat to medium. Place chicken, breast side up, on grill. Cover grill; cook 20 minutes. Turn chicken, breast side down. Cover grill; cook 10 to 15 minutes longer or until brown and juice of chicken is clear when thickest piece is cut to bone (170°F for breasts; 180°F for thighs and drumsticks). Cut chicken into 4 quarters to serve.