Grind the allspice berries. Use a small food processor of spice grinder to coarsely grind the allspice berries (see notes). Transfer to the bowl of a large food processor.
Prepare the marinade. Add the onion, scallions, Scotch Bonnet Chiles (or Habaneros), garlic, Chinese five-spice, pepper, nutmeg, thyme, salt, and sugar to the bowl of your food processor with the ground allspice berries. Pulse and process until everything is coarsely chopped and combined. With your food processor running, add 2 tablespoons of olive oil and the soy sauce to the marinade. Remove lid and double check that all the ingredients have been fully processed. Set aside.
Marinate the chicken. Transfer the chicken to a large baking tray, mixing bowl, or heavy-duty ziplock bag. Drizzle with the remaining 2 tablespoons of olive oil and a light sprinkle of salt and pepper. Pour the marinade over the chicken, mixing and turning well to coat the entire surface of the chicken with marinade. Cover and transfer to the refrigerator to marinate for at least 4 hours to overnight.
Prepare the grill. Remove chicken from the refrigerator and allow it to come to room temperature. Clean grill grates and preheat grill to medium-high heat.
Grill the chicken. When ready to cook, transfer chicken pieces to your grill. Discard marinade. Cook for approximately 5-7 minutes undisturbed before flipping and cooking the other side for an additional 5 minutes. Reduce heat to medium-low and cover your grill. Allow chicken to cook low and slow, checking every 3-5 minutes for hot spots, and flipping as needed, until internal temperature of chicken reaches approximately 157-160 degrees F. as read with a digital thermometer. Immediately remove from the grill to a clean baking sheet or pan and cover with foil for 3-5 minutes to allow chicken to rest and finish cooking. Serve warm with Jamaican Rice and Peas, fresh lime wedges, or other favorite sides. Enjoy!