To make the marinate: In a food processor or blender puree the scallion, the chiles, the soy sauce, the lime juice, the allspice, the mustard, the bay leave, the garlic, the salt, the sugar, the thyme, and the cinnamon.
Put the chicken parts in a heavy-duty resealable plastic bag and spoon the marinade over them, coating them well. Seal the bag, pressing out the excess air, and let the chicken marinate, chilled, turning the bags over several times, for at least 24 hours and up to 2 days.
On an oiled rack set 4 to 6 inches over glowing coals, grill the chicken, in batches if necessary, and covered if possible, for 10 to 15 minutes on each side, or until it is cooked through. Transfer the chicken as it is cooked with tongs to a heated platter; keep it warm, covered loosely with foil, and garnish the platter with the additional chiles.