Peel, wash and chop the celery and potatoes. Peel and chop the onion. Drain chestnuts from the jar. Put 3 chestnuts aside.
Heat 2 tablespoons of oil in a saucepan. Brown onion, celery, potatoes and chestnuts in it. Stir in wine, approx. 1 1⁄2 l water and stock, bring to the boil. Cover and simmer for about 25 minutes.
Cut the remaining 3 chestnuts into thin slices. Fry in 2 tablespoons of hot oil for 2-3 minutes. Set aside. Wash and chop the parsley.
Finely puree chestnut soup and refine with cream. Season to taste with salt and pepper. Arrange the soup, garnish with parsley and chestnut slices with oil.