Mix the spinach and pesto together in a bowl; spread half the mixture into the bottom of a glass baking dish. Place the chicken breasts onto the spinach mixture; top with the rest of the mixture. Cover the dish with aluminum foil.
Bake in the preheated oven until the chicken is no longer pink in the center and the juices run clear, about 30 minutes. Uncover and sprinkle the Parmesan cheese. Return to the oven and bake until the cheese has begun to melt and brown, about 15 minutes.
