Place the potatoes in a large saucepan and add enough cold water to cover by 1 inch. Season the water generously with salt. Bring to a boil and immediately reduce the heat to a gentle simmer. Cook until potatoes are tender, about 10 minutes. Drain the potatoes and transfer to a large bowl. While potatoes are hot, add the vinegar and toss gently with a rubber spatula so the potatoes absorb all that vinegar flavor.
Meanwhile, mix together the mayo, pesto, capers, Dijon and lemon zest and juice.
Drain any excess vinegar that the potatoes haven't absorbed, then mix the potatoes with the dressing and season to taste. Top with crushed kettle chips.