Preheat oven to 350°.
Heat oil in a nonstick skillet over medium-high heat. Add onion; sauté 4 minutes or until tender. Add garlic; sauté 1 minute. Combine onion mixture, chicken, salt, and pepper.
Spread 1/4 cup Green Chile Sauce over bottom of an 11 x 7-inch baking dish coated with cooking spray. Arrange 2 tortillas over sauce; top evenly with half of chicken mixture and 1/2 cup Green Chile Sauce. Repeat procedure, ending with tortillas. Spread remaining sauce over tortillas. Sprinkle with cheese.
Bake at 350° for 20 minutes or until thoroughly heated. Cut each tortilla stack in half.