3 tablespoons butter
3 large leeks (white and pale green parts only), halved lengthwise, thinly sliced (about 4 1/2 cups)
4 medium potatoes (about 18 ounces total), peeled, diced
4 1/2 cups (or more) chicken stock or vegetable broth
2 tablespoons chopped fresh chives
Melt butter in heavy large saucepan over medium heat. Add leeks; stir to coat with butter. Cover saucepan; cook until leeks are tender, stirring often, about 10 minutes. Add potatoes. Cover and cook until potatoes begin to soften but do not brown, stirring often, about 10 minutes. Add 4 1/2 cups stock. Bring to boil. Reduce heat, cover and simmer until vegetables are very tender, about 30 minutes. Puree soup in batches in processor until smooth. Return to saucepan. Thin with additional stock if soup is too thick. Season with salt and pepper. (Can be prepared 1 day ahead. Cover and refrigerate.) Bring soup to simmer. Ladle into bowls. Garnish with chives and serve.