In a large bowl, whisk together olive oil, vinegar, garlic, 3/4 tsp. salt, and 1/2 tsp. pepper. Add thyme and steak; turn to coat. Chill, covered, at least 4 hours and up to 12 hours. Let stand at room temperature during last hour.
Heat a grill to high (450° to 550°) and oil cooking grates, using a wad of oiled paper towels and long tongs. Lift steak from marinade, letting excess drip off, and season generously with salt and pepper. Grill, covered, turning often (watch for flare-ups), until lightly charred, 5 to 10 minutes for medium-rare.
Transfer meat to a cutting board and let rest 5 minutes. Very thinly slice across the grain and at a slant.