Preheat oven to 375°F.
In a large bowl combine shredded chicken, 2 cups of the mozzarella and 2 cups of the Monterey jack cheese, sour cream and taco seasoning. Mix until well incorporated.
Wrap tortillas in a damp paper or tea towel and microwaves for 1 minute.
In a skillet, warm the enchilada sauce. Working with one tortilla at a time, dip it in the enchilada sauce until lightly coated. Scoop ⅓ cup of the enchilada filling into the tortilla and roll tightly. arrange (see side down) in a 9X13 baking dish and repeat with remaining tortillas.
Pour remaining enchilada sauce over the prepared enchiladas followed by the remaining cheese.
Bake for 25 minutes, until cheese is bubbling.