Rinse turkey; pat dry. Turn wings back to hold neck skin in place. Return legs to tucked position. Brush turkey with oil. Season with salt and pepper. Preheat grill to medium heat for 10 minutes or until grill temperature reaches 375  to 400ºF. Turn off middle burner so that only front and back burners are lit.
Place turkey, breast side up, in a roast holder set inside a large heavy-gauge foil pan. Place in center of grill. Grill for 1 3/4 to 2 1/2 hours (11 to 13 minutes per pound) or until turkey is cooked through (180°F in thigh and 170°F in breast). Remove turkey from grill; let stand 15 minutes before carving.