Melt butter in a large skillet over medium heat; add onion, and saute 5 minutes. Add green chiles; saute 1 minute. Stir in cream cheese and chicken; cook, stirring constantly, until cream cheese melts.
Spoon 2 to 3 tablespoons chicken mixture down center of each tortilla. Roll up tortillas, and place, seam side down, in a lightly greased 13- x 9-inch baking dish. Sprinkle with Monterey Jack cheese, and drizzle with whipping cream.
Bake at 350° for 45 minutes.