In a large saucepan, bring 5 cups water, the potatoes, leeks, zucchini and 2 teaspoons salt to a boil. Lower the heat and simmer until the vegetables are tender, about 30 minutes. Let cool slightly.
Using a blender and working in batches, puree the soup. Refrigerate until chilled. Serve with a dollop of yogurt and a sprinkle of chives.