Preheat the oven to 375°F. Lightly grease a 9x13-inch baking dish with cooking spray.
In a large bowl, combine the shredded chicken, green chiles, cream cheese, cilantro, and lime juice. Mix until evenly combined.
To soften the tortillas, place them on a plate and cover with a damp paper towel. Microwave for 15–30 seconds, until warm and pliable.
Spoon about ½ cup of the chicken mixture down the center of each tortilla. Roll them up and place seam-side down in the prepared baking dish. Repeat with all the tortillas until the filling is used up.
Pour the green chile sauce evenly over the enchiladas. Sprinkle the reserved 1 cup of Monterey Jack cheese over the top.
Bake for 25–30 minutes, until the enchiladas are hot and bubbly and the edges are lightly golden.
Let cool for a few minutes before serving. Top with cilantro before serving if desired.