Put the potatoes in a 4- to 5-quart saucepan and cover by about 2 inches with cold water. Add salt if desired and bring to a boil over medium-high heat. Boil gently until the potatoes are tender enough to pierce easily with a skewer, about 20 to 25 minutes, depending on size. Don’t overcook them or they will fall apart.
In a medium mixing bowl, combine the vinegar, lemon juice, lemon zest, chives, & salt.
Drain the potatoes in a large colander and let them cool slightly. When the potatoes are cool enough to handle, cut in bite-size chunks.
Drop the potatoes into the bowl and add the olive oil. Toss to combine. (It may appear that there’s too much dressing, but it will be absorbed.) Let the salad sit for 20 minutes. Season to taste with black pepper and more salt, if necessary. Serve warm or at room temperature with additional chives over the top.
Note: The olive oil may thicken if stored overnight in the fridge. A quick zap in the microwave to bring it back up to room temp could help to quickly restore, or a short sit on the counter will do the same in a bit more time.