Heat oven to 400°F. Place chicken, breast side down, on cutting board. Using heavy-duty kitchen scissors or poultry shears, cut closely along one side of backbone from thigh end to neck. Repeat on other side. Remove backbone, and discard. Turn chicken over so breast side is up; press down to flatten breast area by pressing firmly with heel of hand. Rub chicken with 1 tablespoon of the oil.
Heat 12-inch cast-iron skillet over medium-high heat until hot; place chicken breast side down. Season side facing up with 1 tablespoon chicken seasoning; top with 10-inch heavy skillet to weigh down. Cook 5 to 7 minutes or until skin is golden brown. Remove smaller skillet, and transfer chicken to plate.
In medium bowl, toss potatoes, onion, remaining 2 tablespoons oil, the thyme, salt and pepper until mixed well. Arrange vegetable mixture in single layer in the 12-inch cast-iron skillet. Place chicken, breast side up, on vegetables, and sprinkle top with remaining 1 tablespoon chicken seasoning.
Roast uncovered 45 to 55 minutes or until juice of chicken is clear when thickest pieces are cut to bone (at least 165°F), and vegetables are tender and lightly browned. Garnish with additional thyme leaves, if desired.