Stir together 1 cup shredded Monterey Jack cheese, chicken, sour cream, and green chiles. Spoon chicken mixture evenly down center of each tortilla, and roll up. Arrange seam side down in a lightly greased 13- x 9-inch baking dish. Brush tops of rolled tortillas evenly with butter.
Bake, uncovered, at 350° for 15 minutes or until lightly browned. Pour enchilada sauce evenly over top, and sprinkle evenly with remaining 1 cup cheese. Bake 15 more minutes or until bubbly. Garnish, if desired.