Melt the chocolate in a saucepan with the milk. Away from the heat, stir slowly and carefully until smooth. Allow to cool to lukewarm. Whip the cream until it is a soft snow, then mix in the chocolate.
Divide half the mixture between 6 little pots. Place a teaspoon of chestnut purée in each. Cover with the remaining chocolate and place in the refrigerator to firm. Serve with cream.