Begin by preheating your oven to 375°F (190°C).

In a large mixing bowl, combine the shredded chicken, taco seasoning, sour cream, and 1 ½ cups each of the shredded mozzarella and Monterey Jack cheeses. Stir until the mixture is well incorporated.

To soften the tortillas, wrap them in a damp paper towel or tea towel and microwave them for 1 minute.

In a skillet, gently warm the green enchilada sauce over medium heat. One at a time, dip each tortilla into the sauce until lightly coated. Then, spoon approximately ⅓ cup of the chicken filling into each tortilla and roll them tightly. Place the rolled tortillas seam side down into a 9x13-inch baking dish. Repeat with the remaining tortillas.

Once all tortillas are arranged in the dish, pour the remaining enchilada sauce over the top and sprinkle with the remaining shredded cheese.

Bake the enchiladas for 25 minutes, or until the cheese is melted and bubbly, and the edges of the tortillas have begun to crisp.