Remove steaks from the refrigerator 30 minutes before cooking, allowing them to warm to room temperature.

Heat half of the grill to medium-high and leave the other side off.

Brush the steak with oil, and season with salt and pepper.

Grease the grates with oil, and then place the chuck eye steaks on the cool side for 25 minutes.

Then move the steak to the hot side and sear for about 2 minutes on each side.

Insert an instant thermometer into the thickest part of the steak. Remove from the grill at 120°F (49°C) for rare, 130°F (54°C) for medium-rare, and 140°F (60°C) for medium.

Transfer the steak to a plate, let it rest for 5 minutes. Slice against the grain to serve.