Place the eggs in a medium saucepan in a single layer and add enough cold water to cover by 1 inch.
Bring to a boil over medium-high heat, then remove from the heat and let sit in the hot water for 12 minutes.
Drain the eggs and run them under cold water until they’re cool enough to handle.
Transfer them to the refrigerator for 20 minutes or until completely cool.
Crack and peel each hard-boiled egg.
Using a sharp knife, slice the eggs in half lengthwise. Scoop out the yolks and place them in a medium mixing bowl; reserve the empty egg-white halves on a serving tray.
Mash the yolks with a fork and add the mayonnaise, mustard, capers, and tarragon.
Mix thoroughly with the fork until smooth. Season with salt and pepper.
Fill each egg-white half with 1 heaping teaspoon of the yolk mixture, rounding the tops with a spoon.
Garnish each with a sprinkling of the minced chives and enjoy!