Place potatoes in a large pot of cold salted water. Bring to a boil over high heat. Reduce heat to medium and simmer until potatoes are soft but not mushy, 15 to 20 minutes. Do not overcook.
In a large bowl, whisk mayonnaise, buttermilk, garlic, parsley, chives and vinegar. Season generously with salt and pepper.
Drain potatoes well and let cool for 10 minutes. Add potatoes and celery to bowl and gently toss with dressing. Season with salt and pepper and serve at room temperature.
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