Preheat oven to 350 degrees F (175 degrees C). Spray a 9x13 inch baking dish with nonstick cooking spray.
Mix the cream cheese, Cheddar cheese, green chilies, chili powder, enchilada sauce, button mushrooms, and heavy cream in a large bowl. Arrange chicken breasts in the prepared baking dish; pour sauce over.
Bake in preheated oven until the juices run clear, about 40 minutes.