Place the eggs in a large pot and cover with cold water by 1 inch.
Bring to a boil over high heat, then cover, remove from the heat and let stand for 12 minutes.
Drain the eggs and transfer them to a bowl of ice water for 5 minutes to stop the cooking.
Peel the eggs once cool enough to handle, then slice each one in half lengthwise.
Scoop the yolks into a bowl, keeping the whites intact on a tray.
Mash the yolks with a fork until no large lumps remain, then stir in the mayonnaise, mustard, vinegar, salt and pepper until smooth.
Spoon or pipe the yolk mixture back into each egg white half, mounding it slightly above the surface.
Dust the tops with smoked paprika and scatter the chives over the platter.
Cover loosely and chill for at least 15 minutes before serving, so the filling firms up enough to hold its shape.
Good to Know
Boil and peel the eggs up to two days ahead and store the whites and yolk filling separately in the fridge; fill them the morning of the party so they look freshly made.