In a large pot, add the butter, sliced shallots and thyme and cook on a high heat for 1-2 mins. Add the Madeira and reduce until a glaze. Then add the sliced cooked chestnuts, stock and cream. Boil and blend.
To poach the eggs, stir a large pot of boiling water with addition of white wine vinegar. Add the eggs one by one and poach for approximately 2.5 mins.
Place one egg into the centre of each bowl and cover with the hot chestnut soup.