Clean the leek, cut it lengthways, wash it thoroughly and cut it into slices. Peel the potatoes and cut into small cubes.
Melt the butter in a saucepan. Add the leek and potatoes and sauté gently. Pour in the broth and cover and simmer over low heat for about 15 minutes. Puree the soup with the blender. Season with salt, pepper and marjoram and fold in the cream.
Wash the chives and cut into small rolls. Serve the soup and sprinkle the chives on the soup.