Cut each cooled and peeled hard-boiled egg into two halves. Scoop out the yolks and transfer them to a medium-sized bowl.
Add the softened Philadelphia cheese and chicken breast to the bowl with the yolks, then mix with an immersion blender or hand mixer.
Add the paprika plus salt and pepper to taste and mix well.
Transfer the yolk mixture back into the egg white halves being gentle not to break them.
Cut a black olive in half across the middle. Place one half on the yolk mixture for the body of the spider, then cut the other half of the olive into 8 slices to form the legs. Cut each slice in half again if they're too long.
Alternatively, cut some thin slices of red onion to make red spider legs for an extra-creepy look.