Heat oven to 400° F. Heat the oil in a large ovenproof skillet over medium-high heat. Season the chicken with ½ teaspoon salt and ¼ teaspoon pepper. In batches, cook the chicken, skin-side down, until browned and crisp, 8 to 10 minutes. Transfer to a plate.
To the skillet, add the asparagus, tomatoes, and thyme. Top with the chicken and roast until cooked through, 20 to 25 minutes. Serve sprinkled with thyme.