Wash and trim the leeks and slice the white parts very finely. Melt the butter in a saucepan large enough to contain all the ingredients and stew the leeks until soft. Add the potatoes and stir to mix. Pour in the stock and season with salt and pepper. Bring to a boil, then simmer 40 minutes.
Allow to cool a little, then whizz the whole lot in a blender until smooth. Leave to get cold, and stir in the cream. Check the seasoning, adding some pepper. Chill thoroughly for 6 hours to overnight. Serve in nice little bowls with snipped chives sprinkled on top.