Peel and thinly slice the potatoes. Remove the tops from the leek and finely chop the white bulbs only.
Heat the butter in a large saucepan. Add the potatoes and leek and cook gently, without browning. Add the chicken stock, bring to a boil and then reduce to a simmer. Once the vegetables are tender(about 30 mins) puree them in 2 batches in a blender. Stir in the cream and pureed veggies into a bowl, cover the bowl with plastic wrap and cool the mixture in the refrigerator. If soup is too thick, prior to serving, stir in a bit of water to thin it out.
Serve the mixture in chilled dishes and garnish with the chives.