Begin by massaging chicken with the red palm oil, making sure every surface is coated.
Place the allspice into a mortar and pulverize it; then place the thyme into the mortar and do the same. (You may use an electric coffee grinder or a food processor for this step, however your grinder should be one only used for spices otherwise the quality of your coffee may suffer.)
Finely mince the garlic, onion, and pepper if you like it hot, then combine with the allspice and thyme. To minimize the heat remove the pith before mincing – it is the white rib of peppers not the seeds that are the hottest.
Combine all the remaining ingredients and slather 1½ Tablespoons of the mixture over the chicken, turning it over to coat the underside as well. Set aside any remaining sauce in a covered container and refrigerate.
Place the chicken in a glass baking dish, cover with plastic wrap (you may also use a sealable, gallon size plastic storage bag) and place into the refrigerator overnight.
The next day, remove the baking dish with the chicken from the refrigerator approximately 45 minutes before cooking to allow the meat to reach room temperature. You can either bake or grill the chicken.