Cook potatoes in large pot of boiling salted water until just tender, about 25 minutes. Drain and cool slightly. Transfer to large bowl, add vinegar and toss to coat. Fold in the celery and peas.

Whisk together the mayonnaise, mustard, oil and chives in small bowl until thoroughly blended. Add mayo dressing to the potato mixture and fold together well. Taste and season with salt and pepper. Cover and chill for at least 1 hour to allow flavors to meld and develop. This potato salad is best served cold but not straight out of the fridge. Can be made 1 day ahead. Store refrigerated in an airtight container until needed.