How to Make It
Melt the butter in a large saucepan. Add the leeks and potatoes, season with salt and pepper and cook over moderately low heat, stirring occasionally, until the leeks are softened, about 8 minutes. Add the chicken stock and water and bring to a boil over high heat. Reduce the heat to moderately low and simmer until the potatoes are tender, about 15 minutes. Add the radish greens and crème fraîche and simmer for 2 minutes longer.
Working in batches, puree the soup in a blender on low speed until smooth and flecked with bits of green. Transfer to a large bowl, season with salt and pepper and refrigerate, stirring occasionally, until chilled, about 1 hour. Ladle the chilled soup into bowls, top with the chives and serve.