Special equipment: We recommend using a charcoal grill for this recipe, but a gas grill works well, too.
If you are grilling with charcoal, consider buying lump charcoal, or charred pieces of wood that burn hotter and cleaner than briquettes, which are uniform black pillows made from carbonized wood and a starchy binder. If you do buy briquettes, avoid the self-lighting ones laden with chemicals.
A chimney starter, which looks like a large beer stein, is handy for lighting the charcoal. Use newspaper to get the fire going in the chimney starter.
You'll need a meat thermometer to know when the prime rib has reached a perfect medium rare.
A disposable foil pan makes a handy drip pan, used to catch fat that falls from the meat.
1 (4-rib) standing beef rib roast (about 8 to 12 pounds)
2 tablespoons olive oil
2 tablespoons kosher salt
1 1/2 teaspoons freshly ground black pepper
Horseradish-Cream Sauce, for serving
Rinse the rib roast with cool water and pat it dry with paper towels. Place on a wire rack set on a baking sheet, cover with dry paper towels, and refrigerate until the surface of the meat is dry to the touch. (You can age the meat for several days by tightly covering it with a clean, dry kitchen towel and refrigerating it on a wire rack set on a baking sheet.)
Remove the roast from the refrigerator, unwrap it, and rub it all over with oil, then salt and pepper. Let sit for 1 hour at room temperature.
Twenty minutes before the roast has come to room temperature, prepare the grill. If using a charcoal grill, light enough charcoal to fill a standard chimney starter, about 5 quarts. After about 10 minutes, when the charcoal is red hot, carefully transfer it to one side of the grill's charcoal grate. Set a drip pan next to the hot charcoal. Set the cooking grate over both the charcoal and the drip pan.
Place the roast bone side down on the cooking grate and over the drip pan (not over the flaming charcoal) and cover the grill. Rotate and flip the meat every 30 minutes so that every side of the roast is exposed to the hot side of the grill. Continue flipping until a thermometer inserted into the center of the roast (but not touching any bones) reads 125°F for medium rare, about 2 hours. (Depending on the charcoal you use, you may need to add more halfway through the cooking time.)
Transfer the roast to a cutting board, tent with foil, and let rest 10 minutes. Separate the ribs by cutting through the meat in between them. Slice the meat off the bone and serve with horseradish-cream sauce.