In a medium bowl combine the marinade ingredients.
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Place the chicken legs in a large, resealable plastic bag and pour in the marinade. Press out the air and seal the bag tightly. Turn the bag to distribute the marinade, place the bag in a shallow dish, and refrigerate for 2 to 4 hours, turning occasionally.
Prepare the grill for indirect cooking over medium heat (350° to 450°F).
Remove the chicken from the bag and discard the marinade. Brush the cooking grates clean. Grill the chicken, skin side down first, over direct heat, with the lid closed, until golden brown, 8 to 10 minutes, turning once. Then move the chicken over indirect medium heat, close the lid, and continue cooking until the juices run clear and the meat is no longer pink at the bone, 40 to 50 minutes. Remove from the grill and let rest for 3 to 5 minutes. Serve warm.