In a 6-quart saucepan, sauté white part of leeks and onion in butter for about 5 minutes; do not brown.
Put about 1 cup of the chicken broth into a blender with the sautéed leeks and onions and blend until smooth. Put this back into the pan with the rest of chicken broth and add the potatoes. Cook until potatoes are tender. Add canned milk until you reach desired consistency. Add salt and pepper to taste. Top with cheese and chopped chives.