First combine first 7 ingredients; let stand five minutes. Set aside.
Sauté onion and garlic in hot oil in a large skillet over medium-high heat
for 3 to 4 minutes or until tender. Add salsa, chili and green chiles; reduce
heat and simmer 3 to 4 minutes.
Line the bottom of an 11 x 7-inch baking dish with 3 tortillas; layer with
one-half chili mixture, one half chicken mixture and 1/3 of the cheese. Repeat
layers; top with remaining tortillas. Sprinkle remaining cheese on top.
Bake 350 degrees F for 25 to 30 minutes; let stand 5 to minutes before serving.