Place eggs in a small pot and cover completely with water. Set over medium-high heat and bring to a boil, then turn off the heat and let the eggs cool completely in the water.
Peel eggs, being careful not to break the whites. Rinse under cold water to wash off any remnants of shell. Cut each egg in half lengthwise and scoop out the yolks.
Transfer the yolks to the bowl of a food processor with the mayonnaise, Dijon, and lemon juice. Puree until smooth (Alternatively, everything can be mashed in a bowl with a fork, until smooth). Taste and season with salt and pepper.
Spoon the egg yolk mixture into the egg whites, using it all. Sprinkle with chives and paprika, to taste and serve.
Notes
Storage: Once the eggs are cooked, you can make the yolk mixture and keep it and the egg whites in the refrigerator for up to 3 days. Let the yolk mixture come to room temperature before serving.