Preheat the oven to 400 degrees F (200 degrees C). Grease a large baking dish with cooking spray.
Combine provolone cheese, black olives, and pepper in a small bowl. Combine Parmesan cheese and mozzarella cheese in another small bowl. Place beaten eggs and bread crumbs in separate shallow dishes.
Cut a slit along the thin, long edge of each chicken breast, almost through to the other side. Open each breast and place 1/4 of the provolone cheese-olive filling in the center. Close each breast over the filling and press the edges together. Dip both sides first in beaten egg, then dredge both sides in bread crumbs.
Heat olive oil in a large skillet over medium heat. Add breaded chicken breasts and cook until browned, about 2 minutes per side.
Pour 1/2 of the pasta sauce into the baking dish. Add chicken breasts and pour remaining pasta sauce over each breast. Cover each breast with Parmesan-mozzarella cheese mixture.
Bake in the preheated oven chicken is no longer pink in the center and the juices run clear, about 25 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).