Make the Filling: Cut the hard-boiled eggs in half and remove the yolks. In a bowl, mash the yolks with mayonnaise, Dijon mustard, salt, and pepper until smooth and creamy. Spoon or pipe the mixture evenly into the egg white halves.
Prepare the Olives: Slice 6 whole olives in half lengthwise to create 12 oval bodies. Slice the remaining olives crosswise into thin crescent shapes for the legs (8 legs per spider). Slice small rings from olive ends for the eyes.
Assemble the Spiders: Place one olive half on top of each deviled egg for the body. Arrange 4 olive legs on each side, pressing gently into the filling. Add two small olive rings for eyes and a tiny dot of mayonnaise in the centers.
Garnish & Serve: Dust with paprika, sprinkle with chopped chives, and serve immediately or refrigerate until ready to serve.