Combine the leeks, potatoes and chicken stock in a heavy bottomed 3-quart saucepan. Bring to a boil. Season lightly with salt, partially cover and simmer until the potatoes and leaks are tender, 20 to 30 minutes. Taste and correct seasoning.
Puree the soup in a blender or food processor and chill in the refrigerator for at least two hours before serving. When ready to serve, add the heavy cream and mix well. Top each serving with a bit of minced chives.
Makes 6 to 8 servings