Cut tortillas in half; cut halves into 1/4-inch strips. In 3-quart saucepan, heat oil over medium-high heat. Cook strips in oil, 1/3 at a time, until light brown and crisp. Remove from pan; drain on paper towels.
Heat oil remaining in saucepan over medium-high heat. Add onion; cook 2 minutes, stirring frequently. Add garlic and chile; cook 2 to 3 minutes, stirring frequently, until vegetables are crisp-tender. Stir in broth, tomatoes and salt. Heat to boiling. Reduce heat; cover and simmer 15 minutes. Add chicken; heat until hot.
Peel and pit avocado. Cut into 1-inch slices. Divide half of tortilla strips among individual serving bowls; ladle in soup. Top with avocado and cheese; garnish with remaining tortilla strips and cilantro. Serve with lime wedges.