Preheat oven to 350 F. In a large pot of boiling salted water, cook lasagna noodles for 8 minutes. Drain and rinse with cold water to stop cooking drain again. Set aside.
In a medium bowl, stir together ricotta cheese, beaten egg, Italian seasoning, garlic, and parsley.
Spread ½ cup of the marinara sauce in a 9×13 inch-baking dish. Spread each lasagna noodle with 2 tablespoons of the ricotta cheese mixture, sprinkle each with a scant 3 tablespoons of the shredded chicken, and 2 heaping tablespoon of the mozzarella cheese. Roll up filled noodles and place, seam sides down, in prepared baking dish. Spoon the remaining marinara sauce over-roll-ups.
Cover with foil. Bake in preheated oven for 35 minutes. Remove foil, sprinkle with Parmesan cheese. Bake for 10 minutes more. Serve hot.