1. Heat a grill to medium-high.
2. In a bowl or baking dish large enough to hold the chicken, combine the mustard, oil, tarragon and pepper. Stir to mix thoroughly. Add chicken pieces and turn to coat on both sides. Set aside until grill is ready.
3. To create a cool zone for indirect grilling, bank coals to one side of a charcoal grill or turn off one of the burners on a gas grill. Oil the grill grate. Place chicken, skin side down, directly over the hot side and sear on one side, about 5 minutes. Turn and sear on the other side for about 5 minutes. Move chicken to cooler side of the grill, cover and cook until juices run clear when thickest part of the meat is pierced with a knife, about 5 to 7 minutes longer. Remove from grill and serve immediately.
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