1. Put the rub into a large bowl and add the chicken pieces. Cover and marinate for 2 to 4 hours in the refrigerator, turning occasionally.
2. Build a charcoal fire or preheat a gas grill. Remove the chicken from the refrigerator and place the pieces, bone side down, in the center of the cooking grate. You do not need to turn the chicken pieces while they cook.
3. Grill-roast until the thigh meat registers 180°F and the breast meat near the bone registers 165°F (if you cut up chickens). If you don't have a meat thermometer, cook until it is no longer pink inside and the juices run clear when pierced. Remove and let sit for 10 minutes before serving. Serve with the lime wedges.
Grilling Method: Indirect/Medium Heat