Preheat your oven to 375°F (190°C). In a large bowl, mix the cream cheese, sour cream, and ranch seasoning until smooth. Fold in the shredded chicken and ½ cup of the cheddar and Monterey Jack cheeses.
Spoon the chicken mixture evenly into the center of each tortilla. Roll up the tortillas tightly and place them seam-side down in a greased 9x13-inch baking dish.
Pour the enchilada sauce evenly over the rolled tortillas. Sprinkle the remaining cheese on top.
Bake for 20–25 minutes, or until the cheese is melted and bubbly. Let cool for a few minutes before serving.
Garnish with sliced green onions or fresh cilantro if desired. Serve hot with a side of rice, beans, or a fresh salad.