Preheat oven: Preheat your oven to 375°F (190°C).

Prepare filling: In a large bowl, combine shredded chicken, red enchilada sauce, diced green chiles, and both shredded cheeses. Mix well.

Assemble enchiladas: Heat a skillet over medium heat. Dip each tortilla in olive oil, turning to coat both sides. Place the tortilla in the skillet and heat for a few seconds on each side until softened.

Fill and roll: Remove the tortilla from the skillet and place it on a clean work surface. Spoon about 1/3 cup of the chicken mixture onto the tortilla. Roll up the tortilla tightly, tucking in the ends.

Place in baking dish: Place the rolled enchiladas in a greased 9x13 inch baking dish. Pour any remaining enchilada sauce over the enchiladas.

Bake: Bake in the preheated oven for 20-25 minutes, or until the enchiladas are bubbly and the cheese is melted.

Serve: Top with sour cream and serve immediately.

Enjoy your delicious chicken enchiladas!

Optional toppings: You can also add other toppings to your enchiladas, such as chopped onions, cilantro, or avocado.