Bring a large pot of water to a rolling boil. Gently lower the eggs in with a slotted spoon and cook for 12 minutes.
Transfer the eggs to a bowl of ice water and cool for 5 minutes, then peel.
Halve the eggs lengthwise and pop the yolks into a medium bowl. Mash the yolks with a fork until smooth.
Stir in the Greek yogurt, mayonnaise, relish, Dijon, salt and pepper until creamy. Taste and adjust the salt.
Spoon the filling into the egg whites, or pipe it from a zip-top bag with the corner snipped off. Dust with paprika and scatter the chives.
Chill for 20 minutes before serving, or cover and refrigerate up to 24 hours.