In a small bowl, combine the paprika, mustard powder, chile powder, cumin, and black pepper. Rub this all over the chicken and then rub in the olive oil.
Prepare the grill for indirect heat. (If you’re using a gas grill, this means turning off the center burner and reducing the side burners to medium. If you’re using charcoal, place the coals to heat up on one side of the grill.)
Place the chicken, breast-side up, over indirect heat. Cook, turning every 10 minutes, until the juices run clear on the thickest part of the thigh and the chicken is cooked through, and the internal temperature reads 165°F [74°C] on a meat thermometer, about 60 minutes.