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 over medium-high heat, then immediately reduce the heat to a gentle simmer and cook until the potatoes are tender, about 10 minutes.
Meanwhile, mix the celery and onions in a bowl, then season with salt and set aside.
In a medium bowl, combine the mayonnaise, relish, mustard, parsley and pepper to taste. Combine the celery mixture with the mayo mixture. Let this dressing sit for 20 minutes while the potatoes are cooking so the flavors can marry.
Drain the potatoes and transfer to a large bowl. Immediately add the vinegar and toss gently using a rubber spatula so the potatoes absorb all that vinegar flavor.
While the potatoes are still warm, add the dressing and gently fold to combine. Adjust the seasonings.
Spread half of the potato salad in an 8-inch square baking dish. Top each quadrant of the potato salad with 1 cup of each flavor potato chip so you have a different flavor in each quadrant. Plop the remaining potato salad over each quadrant. Lightly spread with the back of a large spoon. Top each quadrant with the remaining crushed chips and serve immediately.