In a large mixing bowl, combine the shredded chicken, cream cheese, sour cream, diced green chilies, taco seasoning, and half of the Monterey Jack cheese. Mix until well combined.
Warm the tortillas in a dry skillet for about 30 seconds on each side until they are pliable.
Spoon about 1/4 cup of the chicken mixture into each tortilla, and carefully roll it up, placing the seam side down in a greased 9x13 inch baking dish.
In a small saucepan, heat the chicken broth and olive oil together. Pour this mixture evenly over the assembled enchiladas.
Top the enchiladas with the remaining Monterey Jack cheese.
Cover the dish with aluminum foil and bake in the preheated oven for 20 minutes.
Remove the foil, and bake for an additional 10-15 minutes, or until the cheese is bubbly and slightly golden.
Once out of the oven, let the enchiladas cool for a few minutes. Garnish with chopped cilantro and sliced jalapeños if desired.