In a heavy stockpot, heat 1/4 inch of oil until very hot. Working in batches, fry tortillas strips until crispy. Drain on paper towels and set aside.
Pour off all but 1 tablespoon of the oil. Fry the chicken on high for about 5 minutes or until it begins to brown. Add the onions and cook another 5 minutes or until brown. Add potatoes and broth; bring to boiling and simmer, covered for 10 minutes.
Add corn, chilies and cilantro or parsley. Return mixture to boiling and simmer another 5 - 8 minutes or until vegetables are tender.
Divide tortilla strips among soup bowls. Ladle soup on top of strips, and squeeze a lime wedge on top of each portion.