Cover eggs with cold water in a saucepan. Bring to a boil, then turn off heat and cover for 12 minutes.
Chill eggs in an ice bath until cool. Peel and chop into bite-size pieces.
Whisk mayonnaise, Dijon, lemon juice, salt, pepper, and paprika in a mixing bowl.
Stir in celery, red onion, chives, and relish until evenly coated.
Fold in chopped eggs gently. Taste and adjust seasoning.
Serve right away or chill 30 minutes to let flavors meld.