Put the leeks, potatoes, celery and onions in a pot. Add mineral water to cover and season with salt and pepper. Cover, bring to a boil and simmer until very tender. Puree and strain into a glass bowl. Thin with the cream, and with more liquid if needed. Let cool, then chill.
Before serving, thin the soup to the desired consistency with more water or milk. (You can also use chicken stock, but if you're trying to be vegetarian, then obviously don't.) Check the seasonings. Serve sprinkled with chives.