Build charcoal fire or preheat gas grill. Using poultry shears or a chef's knife, split chicken down the breast bone to cut the chicken in 1/2. Brush lightly with olive oil on all surfaces and sprinkle with salt and pepper or Classic BBQ Rub. Set aside.
Using a rib holder, place the 4 chicken halves vertically skin-side facing out in each of the 4 slots. The chicken in the holder will resemble slices of toast in an old-fashioned toast holder. Place the rib/chicken holder in the center of the cooking grate over indirect medium low heat (making sure no heat is directly under the chicken.) Grill for 1 hour, or until chicken registers 185 degrees F in the thickest part of the thigh. After 30 minutes, check the internal temperature with an instant-read thermometer. Brush liberally with barbecue sauce during the final 15 to 20 minutes only. If the chicken is sauced too early, it will burn on the outside before the interior meat is cooked through.
Combine paprika, salt, sugar, brown sugar, cumin, chili powder, pepper, cayenne, onion powder, garlic powder, celery salt and oregano in bowl; mix well. For a smoother rub, puree ingredients in a spice grinder until well combined and all pieces are uniform (the rub will be very fine and tan in color). This step is important if adding to any homemade barbecue sauce.
In a large saucepan on the stove, add tomatoes, sugar, molasses, bourbon, ketchup, chile sauce, vinegars, and Worcestershire sauce, stirring after each additional ingredient to combine. Add the classic spice rub and simmer until the flavors have blended and the sauce has thickened somewhat, about 30 minutes.
Let the sauce cool for about 10 minutes or until it is warm but no longer "boiling" hot. Puree using an immersion or traditional blender. Taste and adjust seasonings with salt, about 1/2 teaspoon, and freshly ground pepper. Remember, the ribs will have plenty of spice rub on them, so don't over-season the sauce. Add the cocoa powder and mix well to combine. Let sit 5 minutes and stir again to make sure cocoa powder is well distributed. Let cool and pour into a clean glass jar for storing. The sauce can be made in advance and kept for 2 weeks in the refrigerator.
Extra rub can be stored in an airtight container for up to six months.