Place eggs in a saucepan and cover completely with water. Bring to a boil over high heat. Once the water has reached a boil, set a timer for 6 minutes. Drain the hot water and run the eggs under cold water until they cool down. Once cooled, gently peel the shells from the eggs.
Slice each egg in half, lengthwise. Gently remove the yolks and place them in a mixing bowl.
Whisk the egg yolks with mayonnaise and relish. Adjust the seasoning with salt and pepper to taste. (Add more mayonnaise if needed to reach a creamy consistency.)
Spoon the egg yolk mixture into the egg white halves. Sprinkle with chives.