Preheat oven to 220 degrees C. Grease a rimmed 22cm x 30cm baking tray with cooking spray.
Combine carrots, turnip, potato, onion, 1 1/2 tablespoons olive oil, garlic, 1 tablespoon rosemary, 1/2 teaspoon salt and 1/2 teaspoon pepper; toss until well coated and place on the prepared baking tray.
Bake in the preheated oven until starting to soften, about 15 minutes.
Remove from oven and place chicken thighs on top of vegetables; sprinkle with 1 tablespoon olive oil, 1/2 teaspoon salt, 1/2 teaspoon pepper and remaining rosemary.
Bake in the preheated oven until chicken is crispy and vegetables are tender, about 15 minutes more.