Slice thinly the onion and put it in a thick-bottomed saucepan with extra virgin olive oil. Cook the onion over low heat for a few minutes until golden, then pour in the rice. Toast the rice for a few minutes, stirring constantly with a wooden spoon.
When the rice is toasted and hot pour in the white wine and reduce.
Cook the risotto, adding gradually the hot broth, stirring frequently. It will take about 40 minutes for the rice to absorb all the broth. Cook until al dente.
While the rice is cooking carve the chestnuts with a sharp knife and cook them in a skillet over medium heat - or in the fireplace - until they are slightly charred. Let them cool down slightly and peel them. Chop the chestnuts leaving some of them aside for decoration.
When the rice is ready add the crumbled cheese and stir vigorously with a wooden spoon to cream it. Add also the chopped chestnuts and season with salt to taste, if needed.
Serve the risotto with a few crumbled chestnuts on top.