1. Rinse chicken; cut into 1-inch chunks.
2. Rinse chilies, then trim and discard stems, seeds, and veins. Cut chilies lengthwise into 1/8- to 1/4-inch strips.
3. In a 4- to 5-quart pan over high heat, bring chilies, onion, and broth to a boil. Reduce heat, cover, and simmer 5 minutes. Add chicken, cover, and simmer until meat is no longer pink in center of thickest part (cut to test), about 4 minutes.
4. Meanwhile, cut tortillas into 1-inch squares. Divide squares equally among wide soup bowls.
5. Ladle soup over tortillas. Add lime juice to taste.
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