Place the eggs in a large pot and cover with cold water. Bring the water to a boil over medium heat, then reduce to a simmer and cook for 10 minutes.
Drain the eggs and rinse them under cold running water until cool enough to handle. Peel off the shells and slice each egg in half lengthwise.
Remove the yolks and place them in a mixing bowl. Add the mayonnaise, Dijon mustard, salt, black pepper, and paprika. Mash and stir until the mixture is smooth.
Spoon or pipe the yolk mixture back into the hollows of the egg whites.
Cut four olives in half lengthwise to form spider bodies. Slice the remaining olives into thin strips for legs. Arrange one olive half and several strips on top of each filled egg to create a spider shape.
Scatter the chopped chives over the tray for extra color and a mild onion note.