Trim off the outside leaves of the Brussels sprouts and cut a cross in the stalk.
Plunge into boiling salted water and cook fairly fast until they are just done but not soggy, for about 4-5 minutes.
Refresh the sprouts in cold water and drain. Cut the chestnuts and sprouts in half. Melt the butter in a frying pan and add the sprouts and colour lightly for 5 minutes.
Add the chesnuts and heat through for a couple of minutes. Season and serve hot with the turkey.