1 cup (about) milk
Combine potatoes and broth in heavy 2-quart saucepan. Cover and simmer until potatoes are very tender, stirring occasionally, about 45 minutes. Let mixture cool slightly.
Purée potato mixture in batches in blender or processor. Return soup to saucepan. Stir in enough milk to thin to desired consistency. Mix in butter and chives. Bring to simmer. Remove from heat and mix in 1/3 cup sour cream. Season with salt and pepper. Serve, passing additional sour cream separately.