In a medium saucepan, saute onion and green chile peppers until tender. Stir in chicken, then milk and soup. Heat through, mix well and set aside.
Preheat oven to 350 degrees F (175 degrees C).
In a small skillet, saute tortillas a few at a time until soft. Cut tortillas into quarters, then line a 9x13 inch baking dish with 1/2 of the tortillas. Spread 1/2 of the chicken mixture over the tortillas, then layer with remaining tortillas and remaining chicken mixture. Finally, sprinkle with cheese.
Bake at 350 degrees F (175 degrees C) for 30 minutes, or until cheese is melted and bubbly.