Remove the tough outer leaves and place the sprouts in a pan of boiling salted water. Cover and cook gently for 6–10 minutes, depending on their size, until just tender. (Take care not to overcook them, as overcooked sprouts have an unpleasant taste and smell.)
Meanwhile melt the butter in a saucepan and add the chestnuts. Heat gently until warmed through.
Drain the sprouts and stir into the warmed chestnuts. Season with a little salt and pepper and serve.