In a pot with enough water to cover, boil the chicken 25 minutes, or until juices run clear. Drain, cool, and shred.
Preheat oven to 350 degrees F (175 degrees C). Lightly grease a medium baking dish.
Fill each tortilla with equal amounts of chicken and cheese, reserving 1/4 cup cheese for topping. Roll tortillas to form enchiladas. Arrange enchiladas in the prepared baking dish. Cover with the enchilada sauce.
Bake enchiladas 30 minutes in the preheated oven. Top with reserved cheese, and continue baking 5 minutes, until cheese is melted.