I've been curious about chestnuts and their flour too! Here's a recipe I found, which could be adapted pretty easily, I think:

CHESTNUT CAKE (adapted from Gourmet)

GLUTEN FREE
1/2 C mild olive oil
1 C chestnut flour + add'l for dusting
1/4 C hazelnuts
1/2 tsp baking powder
1/2 tsp baking soda
1/2 tsp salt
3 large eggs, separated
1/2 C mild honey
1/4 C sugar (sub for raw honey??)

Toppings:
powdered sugar or
whipped cream and chopped hazelnuts -- Place an oven rack in the middle position and preheat to 350o F. Spray a 9 - 9 1/2" springform pan with non-stick spray and dust with chestnut flour.
-- Roast the hazelnuts in the oven for 20-25 minutes. Rub the nuts in a kitchen towel to remove the loose skins. Some skin will probably remain. Chop until medium fine in a food processor.
-- Mix together the chestnut flour, baking powder, baking soda and salt. Then stir in the nuts.
-- In another bowl, beat together the egg yolks, oil, honey and 2 tbsp sugar until thick and pale -- about 5 minutes. Add the flour mixture and mix at low speed until well mixed.
-- Beat the egg whites and a pinch of salt in another bowl with clean beaters until they form soft peaks. Add the remaining 2 tbsp sugar a little at a time until the whites hole a soft peak. Fold into the cake mix 1/3 at a time until well mixed. Pour into cake pan. Bake 30 minutes. Then loosely cover with aluminum foil and bake another 10-15 minutes.
-- Place on rack to cool. Remove pan's side.
-- Sprinkle with powdered sugar as shown or top with whipped cream and a sprinkle of chopped hazelnuts.