Melt butter in a large skillet over medium heat. Add onion and garlic; saute until cooked well and golden brown. Add chiles; saute 1 minute. Stir in cream cheese and chicken; cook, stirring constantly, until cheese melts.
Spoon 2 to 3 tablespoons chicken mixture down center of each tortilla. Roll up tortillas; place, seam side down, in a lightly greased 13X9 baking dish. Pour green enchilada sauce over all and sprinkle with Jack cheese; spread with sour cream.