Put potatoes in a large pot, cover with water, salt generously and bring to a boil over high heat. Reduce heat to a brisk simmer. Cook for about 30 minutes, until cooked through but firm. (Test with a skewer or paring knife.) Drain.
Holding each potato in a paper towel or tea towel to keep from burning your fingers, peel the thin skins while still warm with a paring knife (they come away easily). Cut peeled potatoes into thick slices (about ⅜ inch) and place in a large low bowl.
In a small bowl, add vinegar and mustard, stirring to dissolve. Whisk in olive oil and season to taste with salt and pepper. Pour over warm sliced potatoes and very gently and briefly toss with hands, taking care not to break the slices. Sprinkle with a little salt and leave to cool at room temperature.
When potatoes have cooled, add tarragon leaves and chives (save some of the herbs for garnish) and very gently toss again. Taste, adjust for salt and toss one more time. The salad should be fairly oily; drizzle with a little more oil if necessary. Serve at room temperature, sprinkled with reserved herbs.
