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