Brown ground beef in a large skillet, stirring until it crumbles and is no longer pink; drain. Stir in taco seasoning mix and half of chopped green chiles; set aside.
Stir together remaining green chiles, soup, and sour cream. Pour half of soup mixture into a lightly greased 13- x 9-inch baking dish.
Spoon beef mixture evenly down centers of tortillas; roll up. Place, seam sides down, over soup mixture in baking dish; top evenly with remaining soup mixture and cheese.
Bake at 350° for 25 minutes or until thoroughly heated. Garnish, if desired.