To cook the clams, place them in a heavy large skillet. Cover with the water and wine. Bring to a boil, cover the skillet, then reduce heat and simmer for 3 minutes, shaking the skillet occasionally. With tongs, remove the clams that have opened and place them on a tray. Recover and cook for up to 3 to 4 more minutes. Discard any clams that have not opened. Line a fine sieve with a dampened paper towel. Strain the cooking liquid through the sieve into a heavy large saucepan.
For the soup, add the leeks and potatoes to the saucepan with cooking liquid. Bring to a boil, then lower heat and simmer until the potatoes are tender, for about 15 minutes. Add the cream. Coarsely mash the potatoes in the broth to thicken, using a mallet or potato masher. Season with salt and pepper. (This can be prepared ahead and cooled. Cover the clams and soup and set aside at cool room temperature for up to several hours.)
To serve, remove the clams from their shells and mince. Pour any liquid from the shells back into the soup through the sieve and discard the shells. Thin the soup with additional liquid if necessary. Bring to a boil, stirring over medium-high heat. Add minced clams. Ladle into 4 soup bowls. Sprinkle with chives. Serve immediately.