Step 1: Set up your grill for spit-roasting and preheat to medium-high (about 400 degrees). Place a large drip pan in the center.
Step 2: Using the tip of a paring knife, make a series of slits in the roast on all sides. Each slit should be about 1/2 inch wide and deep, and 1-1/2 inches apart. Insert sprigs of rosemary in half the slits; insert garlic slivers in the other half. Generously—and I mean generously—season the roast on all sides with salt and pepper, patting the seasonings into the meat. Drizzle oil over the meat, rubbing it in with your fingertips.
Step 3: Thread the roast from end to end on the rotisserie spit and secure it with the prongs. Fit it in the motor socket and spit holder. If using wood chips with a charcoal grill, toss them on the coals.
Step 4: Spit roast the rib until crusty and brown on the outside and cooked to the desired degree of doneness inside, 1 to 1-1/2 hours for medium-rare. Use an instant-read meat thermometer inserted into the very center of the prime rib through the large end but not touching the rotisserie spit to test for doneness: cook to 120 degrees for rare; 135 degrees for medium-rare. We won’t go any more well done than that. Remember, the prime rib will continue cook even after it leaves the rotisserie.