In a medium sauce pan, cook onion in oil over medium heat until soft. Stir in flour. Add broth and milk; cook, stirring constantly, until thickened. Stir in chilies and tomatoes.
Coat a 9 x 13 inch baking pan with nonstick spray. Place 1 cup sauce in bottom of pan. Layer half the chicken, half the tortilla strips, and 1 1/4 cups sauce. Repeat with remaining ingredients. Top casserole with shredded cheese.
Bake at 350 degrees F (175 degrees C) for 40 to 45 minutes.