Without adding any oil, toast the chestnuts in a frying pan until golden brown. Add the lemon juice, cover and simmer over a low heat for approx. 4 mins. Add the butter, sugar and rosemary, caramelize, season with salt, set to one side.
Bring the stock to the boil, stir in the polenta, reduce the heat, simmer over a low heat for approx. 4 mins., stirring constantly to form a thick purée, season. Scatter the chestnuts over the top, then spread the crème fraîche on top.