With a sharp knife cut along each side of chicken's backbone; remove backbone. Tuck wing tips behind back and place in a shallow casserole.
Grate the rind off of the orange and squeeze out juice. Mix with white wine vinegar, oil, thyme and pepper. Pour over chicken; cover and marinate in refrigerator, turning often, for at least 4 hours or up to 24 hours.
Reserving marinade, place chicken, skin side down, on greased grill over medium-low **indirect heat**. Cover and cook for 1 hour, turning and basting with marinade halfway through.
Transfer to direct heat; cook for 10 minutes per side or until meat thermometer inserted in thigh registers 185°F.
Remove to platter and tent with foil; let stand for 10 minutes before cutting into quarters.
**Indirect heat means heat one side of the grill and cook the chicken on the other side.