Preheat oven to 350°F (175°C) and lightly grease a 9x13 inch baking dish.
In a medium bowl, mix shredded chicken with 1/2 cup of cheese and 1/4 cup of green sauce.
Heat vegetable oil in a skillet over medium heat and briefly fry each tortilla for 5 seconds per side to make them pliable.
Dip a tortilla into the green sauce, fill with 2 tablespoons of the chicken mixture, roll tightly, and place seam-side down in the baking dish.
Repeat for all tortillas, then pour the remaining green sauce over the top and sprinkle with the remaining cheese.
Bake for 20 minutes until the cheese is melted and the sauce is bubbling.
Top with sour cream, diced onions, and fresh cilantro before serving.