In a medium bowl whisk the marinade ingredients.
Using a sharp paring knife, cut a few deep slashes into the meaty parts of each chicken leg. Place them in a large, resealable plastic bag and pour in the marinade. Press the air out of the bag and seal tightly. Turn the bag to distribute the marinade. Refrigerate for 4 to 8 hours, turning occasionally.
Prepare the grill for indirect cooking over medium heat (350° to 450°F).
Remove the chicken from the bag, letting the herbs cling to the chicken. Discard the marinade. Brush the cooking grates clean. Grill the chicken over indirect medium heat, with the lid closed as much as possible, until the juices run clear and the internal temperature reaches 160° to 165°F in the thickest part of the thigh (not touching the bone), 50 minutes to 1 hour, turning once. If desired, to crisp the skin, grill the chicken over direct medium heat during the last 5 minutes of grilling time, turning once. Remove from the grill and let rest for 3 to 5 minutes. Cut into thighs and drumsticks, if desired.
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