Preheat oven to 350 degrees.
Combine chicken, lime juice, chili powder, salt and pepper. Let stand 5 minutes.
Saute onion and garlic in oil in a large skillet over medium-high heat until tender, 3 to 4 minutes. Add salsa, chili and chilies. Reduce heat and simmer 3 to 4 minutes.
Line 11-by-7-inch baking dish with three tortillas. Layer with half the chili mixture, half the chicken mixture and 1/3 of the cheese. Repeat layers. Top with remaining tortillas. Sprinkle with remaining cheese.
Bake 25 to 30 minutes. Let stand 5 to 10 minutes before serving.