Start by combining all the marinade ingredients in a food processor or blender. Blend until you achieve a rough paste. It shouldn’t be completely smooth but mixed enough to coat the chicken evenly.
Place the chicken in a large resealable plastic bag or a dish. Pour the marinade over it, ensuring every part is covered. Seal and refrigerate for at least 8 hours or overnight. The longer, the better as it allows the flavors to develop and soak into the meat.
Preheat your grill by building a two-zone fire if using charcoal or setting one side to medium on a gas grill. This setup allows you to cook the chicken indirectly before finishing it with a direct, high-heat sear.
Place the marinated chicken on the cooler side of the grill, skin side up. Cover the grill and cook for about 45-50 minutes, until the internal temperature of the chicken reaches 145°F. For added smoky aroma, place bay leaves and whole allspice berries atop the charcoals.
Move the chicken to the hotter side and cook skin-side down for 3-5 minutes, until it develops a deep, charred color. Flip it to crisp the other side. Ensure the internal chicken temperature is 165°F before removing it from the heat.
Once done, rest the chicken for 5 minutes to allow the juices to redistribute. This step keeps it moist and flavorful.