Preheat the oven to 180 degrees C, gas mark 4. Grease a 23 cm spring form or cake tin.
Break the chocolate into pieces and melt in the microwave or in a double boiler (au bain-marie), and set aside.
Whisk the egg whites with a pinch of salt until stiff, but not dry.
In another bowl, whisk butter and chestnut puree with the sugar. Gradually whisk in the egg yolks, then add the rum and chocolate.
Stir in a dollop of the egg white, whisk well to mix everything together, then carefully fold the rest of the egg white in the chestnut mixture.
Pour the batter into the tin and let bake for 40 to 60 minutes. You could do the toothpick test, but it should not come out completely clean. Let the cake cool in it's tin on a rack before you unmold it on to a plate.
Decorate with whipped cream and candied chestnuts.