Generously add carne asada seasoning/spice rub all over chicken, making sure you get some under the skin on top. Use your hands to rub it into the chicken. Place in baking pan with cover or heavy plastic storage back. Marinate overnight.

Remove chicken from refrigerator 1 hour before cooking. Set up your grill for indirect grilling at a temperature of 250 degrees F. If you want to add some smoky flavor, add a few applewood chunks near the hot coals 5 minutes before adding chicken. Or if cooking on gas grill add wood chips to a smoker box. Close lid for a few minutes.

Brush grates on cool side with oil. Add the chicken, skin side up on cool side of the grill. Close lid and cook for about 2 hours or until internal temperature of chicken reaches 165 degrees. Pull off the chicken as it reaches the desired temperature. When done, transfer chicken to a dish, cover loosely and let rest for 5 to 7 minutes. Yields 4 servings.