Make the jerk seasoning by combining the salt, allspice, brown sugar, onion granules, garlic, nutmeg, pepper, ginger, cayenne pepper, cinnamon and thyme. Toss the chicken pieces with the spice mixture; cover and marinate in the fridge for 2 to 4 hours.
Preheat oven to 180 C / Gas 4. Pour the vegetable oil into a baking dish.
Place the chicken pieces skin-side up into the baking dish. Bake in the preheated oven for 1 hour 20 minutes, until cooked through. Turn on the oven grill; cook until the skin crisps, 2 to 5 minutes.