Preheat the grill to high heat.

Season the turkey with olive oil, salt, and pepper. Let stand at room temperature for 20 minutes.

Mix the rice, chestnuts, onion, and herbs together in a baking dish. Top with crumbled goat cheese. Cover with foil and set aside. Preheat the oven to 350 degrees F.

Place the turkey on the grill and grill each side over high heat until nicely browned, about 4 to 5 minutes on each side. Turn the heat down to low and move the turkey pieces to a higher rack in the grill. Close the lid of the grill and let cook slowly, turning occasionally, for 30 to 40 minutes. Then begin brushing the pomegranate juice on the turkey and continue until the turkey is cooked through; an instant-read thermometer inserted into the thickest part of the thigh, away from the bone should register 175 degrees F. Remove the turkey from the grill, transfer to a cutting board, and let it stand, loosely covered with foil, for 15 minutes before carving.

Place the stuffing in the oven and let warm for 10 minutes. Serve stuffing with turkey. Bring any remaining pomegranate juice to a simmer and drizzle over the turkey.