Make the jerk seasoning:
Crush the cloves and allspice in a mortar (or put them in a plastic bag and crush them with a rolling pin) to break the berries. Put these and the remaining ingredients in a food processor or blender. Process or blend for a few minutes until puréed to a somewhat coarse paste; scrape the sides as necessary (avoid inhaling the potent fumes).
Grill the chicken:
Mix about 3/4 cup of the jerk paste with the vegetable oil in a bowl. Rub the paste all over the chicken, including under the skin, so it’s lightly coated. Refrigerate for 30 minutes to 1 hour.
Meanwhile, prepare the grill. For charcoal, start the coals in a chimney starter, and when they’re glowing, after about 30 minutes, dump them out and spread in an even layer. For gas grills, set two burners to medium hot and another to medium.
When the coals are medium-hot or the gas grill is ready, put the chicken, skin side down, over the hotter part of the grill (cover the grill, if using gas). When the skin has begun to brown, after about 2 minutes, rotate each piece slightly so the skin doesn’t burn or stick. When the skin browns more, after about another 2 minutes, turn each piece over. Grill until the second side is browned, about another 4 minutes. Move the chicken to the cooler part of the grill (you might want to turn one gas burner down to medium to accommodate all the pieces) and cover. Grill until an instant-read thermometer inserted in the thigh reads 165°F (or cut into the joint and check that the juices run clear), another 10 to 20 minutes. If the non-skin side starts to burn, turn it back over to the skin side, or move it to a cooler spot. Let the chicken rest, covered, for 5 minutes before serving.
The jerk seasoning can be refrigerated for up to three months in a tightly sealed container.