Make the Marinade: Blend Scotch bonnet peppers, allspice, garlic, ginger, brown sugar, thyme, scallions, lime juice, soy sauce, nutmeg, cinnamon, salt, and pepper into a smooth paste.
Marinate the Chicken: Rub the marinade thoroughly onto the chicken pieces. Cover and refrigerate for at least 4 hours, preferably overnight, to let the flavors infuse.
Prepare the Grill: Heat your grill for indirect grilling (medium-high). If using charcoal, wait until the coals are covered with white ash.
Grill the Chicken: Place the marinated chicken on the grill, away from direct heat. Cover and cook for 45 minutes, turning and basting with leftover marinade halfway through.
Rest and Serve: Remove from the grill and let the chicken rest for 5 minutes before serving to allow the juices to redistribute.