Preheat the oven to 200°C, fan 180°C, gas 6. Bring a large pan of water to the boil and add the sprouts. Cook for 5 minutes. Drain and leave to cool for a few minutes.
Spread the sprouts in a roasting tin with the chestnuts. Roast for 15 minutes until golden.
Remove the roasting tin from the oven. Sprinkle the orange zest and Parmesan over the top, then serve.