1. Drop the beans into a large pot of boiling, salted water. Add the potato and cook, uncovered, at a gentle bubble for 10 minutes or until the beans are tender. Remove the potato with a slotted spoon. Drain well and transfer to the container of a blender or processor. Break the potato apart with a fork to release the steam.
2. Drain the beans in a colander set under cold running water. Shake to remove as much water as possible. Transfer the beans to the blender or processor and whirl with the potato until smooth. Return to the pan. Blend in the butter, lemon juice, and cilantro and stir over medium heat to warm through. Season with salt and pepper and transfer to a serving bowl. Sprinkle the surface with chives.