Preheat your oven to 375°F (190°C) and place a rack in the center.
In a large mixing bowl, combine shredded chicken with 1½ cups mozzarella, 1½ cups Monterey Jack, sour cream, and taco seasoning.
Wrap corn tortillas in a damp towel and microwave for 1 minute to soften.
Warm the green enchilada sauce in a small skillet over medium-low heat.
Dip each tortilla in the sauce, then spoon about ⅓ cup of the chicken mixture onto each tortilla, roll tightly, and place seam-side down in a 9x13-inch baking dish.
Pour the remaining enchilada sauce over the top and sprinkle with remaining cheeses.
Bake for 25 minutes until bubbling and cheese is melted and browned. Let sit for 5 minutes before serving.
Garnish with cilantro and red pepper flakes if desired.
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Notes
Store leftovers in the fridge for up to 3 days. Reheat in the oven or microwave.