Cut the green tops from the leeks and cut the white parts into 1-inch lengths. Sauté the white parts gently in butter until soft. Do not allow to brown.
Peel and slice potatoes and add to leeks with chicken stock, and salt, pepper and finely grated nutmeg, to taste, and simmer until vegetables are cooked.
Force the vegetables and stock through a fine sieve, or blend in an electric blender until smooth. Chill. Just before serving, add cream and serve sprinkled with chives.