Coat bottom of non-stick skillet with olive oil. Season chicken breast halves with salt and pepper and saute in heated pan until browned on the outside and no longer pink in the center, about 6 minutes on each side. Set aside until cool enough to handle.
In a medium saucepan, combine the cream of mushroom, cream of chicken, and sour cream over medium heat until heated through.
Meanwhile, cook the egg noodles as the package directs. Once egg noodles are drained, layer them along with a cup of the soup/sour cream mixture into the bottom of a 13x9 inch casserole or Pyrex dish.
Once chicken is cool enough to handle, shred or dice into small pieces and spread atop the egg noodle mixture. Top chicken with the 2 cups of mozzarella, and then pour the rest of the soup mixture on top of the cheese. Shake or poke with fork to get the wet ingredients evenly distributed, but do not mix completely. Top with the 2 sleeves of Ritz-style crackers.
Bake uncovered at 350 degrees for 25-30 minutes until browned. Let stand for 5-10 minutes once removed from oven. Serve and enjoy!