Heat grill to high. Rub both sides of steak with oil, and season generously with salt and pepper. Grill for 5 to 7 minutes per side for medium-rare. Let rest for 10 minutes.
Meanwhile, drizzle onion slices with oil, and season with salt and pepper. Grill, turning occasionally, until cooked through, 6 to 8 minutes per side.
Thinly slice meat across the grain, and serve topped with grilled onion.