Combine the paprika, chili powder, salt, and pepper in a small bowl. Rub the mixture inside and outside the chicken, both over and under the skin. (Be careful not to tear the skin.) Let the chicken sit at room temperature for 30 minutes.
Prepare the grill for indirect cooking, making a hot fire on half the grill and leaving the other half unheated. Place an inexpensive oven thermometer (available at any kitchen supply store) on the cool half of the cooking grate. (You can’t rely on your grill’s built-in thermometer because you want to measure the temperature only on the unheated side. ) Close the grill and heat the temperature to 400°F (200°C) on the unheated side.