Arrange the eggs in a single layer in a saucepan. Cover with cold water by 1 inch and heat uncovered until the water just reaches a boil.
Move the pan off the burner, cover, and leave undisturbed for 12 minutes. Meanwhile, prepare a bowl of ice water.
Transfer the eggs to the ice water and cool for at least 10 minutes. Crack the shells all over, peel gently under cold running water, and dry the peeled eggs thoroughly.
Slice each egg lengthwise and lift the yolks into a bowl. Arrange the 12 white halves cut-side up on a tray. Press the yolks through a fine-mesh sieve or mash with a fork until no large pieces remain.
Stir in the mayonnaise, mustard, vinegar, salt, and pepper until smooth. The filling should hold a soft mound. Spoon or pipe a small amount into every white first, then divide the remaining filling evenly among all 12 halves.
Cover without touching the tops and refrigerate for 20 minutes. Just before serving, dust lightly with paprika and scatter chives over each half.