Peel the potatoes and slice each one lengthwise in half, or in quarters if very large; then cut crosswise into half-round or quarter-round slices, about 1/2 inch thick. Put the slices in a saucepan with water just to cover and 1 1/2 teaspoons of salt per quart of water. Heat to a simmer, and cook the potatoes for 5 to 6 minutes, or until just cooked through. It is essential that they be just cooked through. Bite into a slice or two to be very sure. Immediately remove from the heat and drain the potatoes into a colander, but save a cup of the cooking liquid for dressing the potatoes. Transfer bowl. Stir the cider vinegar and sugar with 1/3 cup of the potato water or chicken stock and drizzle this over the potato pieces, turning them gently to distribute it evenly. Let sit 10 minutes to absorb the liquid.
Add the prepared onion, celery, bacon, pickle, hard-boiled eggs, and chives, and season carefully to taste. Top with 2/3 cup of mayonnaise and, with a large rubber spatula, gently fold everything together until well blended. Taste the salad and add more salt, pepper, or mayonnaise as needed. Cover the salad and set aside in the refrigerator for at least an hour or so before serving.