In a heavy stockpot, heat 1/4" oil until very hot. Working in batches, fry tortilla strips until crisp. Drain on paper towels and set aside.
Pour off all but 1 tablespoon oil. Saute chicken on high 5 minutes or until it begins to brown. Add onions and cook 5 minutes or until brown. Add potatoes and broth. Bring to a boil and simmer, covered, 10 minutes.
Add corn, chilies and cilantro. Return to a boil. Simmer 5-8 minutes or until vegetables are tender. Divide tortilla strips among soup bowls. Ladle soup into bowls, and squeeze a lime wedge on top of each portion.