Place the eggs in a single layer in a saucepan and cover with cold water by about 1 inch. Bring to a full boil over high heat.
Turn off the heat, cover the pan and let the eggs stand for 12 minutes. Move them to a bowl of ice water for at least 5 minutes, then peel.
Cut each egg in half lengthwise. Pop the yolks into a bowl and set the whites on a plate.
Mash the yolks with a fork until fine and crumbly. Stir in the mayonnaise, mustard, vinegar, salt and pepper until smooth.
Spoon the filling into the egg whites, or pipe it in with a zip-top bag with one corner snipped off.
Sprinkle with paprika and chives. Chill until ready to serve.