Slice through the top 1/3 of each cooked egg, ensuring some of the yolk is included in the slice.
Carefully remove the egg yolk from the bottom portion of the egg using a spoon and transfer to a bowl.
Mix egg yolks, mayonnaise, mustard, pickle, horseradish, pickle juice, salt, and pepper together in a bowl.
Fill a piping bag or a plastic bag with a corner snipped with the egg yolk mixture.
Pipe egg yolk mixture into the hollowed egg whites creating the chick, ensuring there is enough filling to add eyes and a beak.
Slice small wedges out of the carrot rounds creating 12 beaks. Add a beak to each chick.
Slice olive pieces into small squares to be used as eyes. Add 2 eyes to each chick.
Place the egg tops onto each chick to look like a chick peaking out of the egg.