Preheat oven to 350 degrees F (175 degrees C). Grease a deep baking dish.
Spread spinach into the bottom of the prepared baking dish. Arrange chicken breasts atop the spinach in a single layer; top with sliced olives. Sprinkle feta cheese over the chicken and olives. Drizzle dressing over everything. Cover dish with aluminum foil.
Bake in preheated oven until chicken is no longer pink in the center and the juices run clear, about 2 hours. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Bring a large pot of lightly salted water to a boil. Cook penne at a boil, stirring occasionally, until tender yet firm to the bite, about 11 minutes; drain and return penne pasta to the pot.
Stir baked chicken mixture with the drained penne pasta.