Preheat the oven 375 degrees F (190 degrees C).
Cut the Chicken (1) into four pieces. Trim off the fat and excess skin. Wash the chicken pieces with juice from the Lime (1) then rinse with cool water. Pat dry and get ready to season.
In a small bowl or plate, mix the Salt (1 teaspoon), Ground Black Pepper (1 teaspoon), Ground Cinnamon (1/2 teaspoon), Dry Mustard (1/2 teaspoon), Ground Allspice (1/2 teaspoon), and leaves of Fresh Thyme (4 sprig), then work it into the pieces of chicken. Be sure to coat both sides of the chicken.
Line the baking dish with aluminum foil. With your oven set at 375 degrees F (190 degrees C), place the baking dish with the seasoned chicken on the middle rack and let cook for 45 minutes.
After 45 minutes, tip the baking dish and spoon out any liquid/fat from the bottom of the dish and discard it. We need to get rid of all liquid as we want the bbq sauce to really stick to the pieces of chicken for that gooey goodness. Using your favorite store Barbecue Sauce (1/3 cup), baste the chicken pieces and place them back in the oven for 10 minutes.
After 10 minutes, turn the pieces of chicken over and give this side a nice coat of that Barbecue Sauce (1/3 cup) and back into the oven for another 10 minutes.
It’s time to flip it over again and give it a final coat of that luscious Barbecue Sauce (1/3 cup). Be generous as we want this to sort of caramelize and form a sticky coating over the pieces of chicken. Back in the oven for 10 minutes.
In the last 3 minutes, turn on the broiler and to get a perfect color on your BBQ chicken.