1. Heat oil in a large saucepan over medium-high heat. When the oil is hot, fry the tortilla strips in batches until golden brown and crisp, about 2 to 3 minutes total. Reserve.
2. Discard all but 1 tablespoon of oil. Turn heat to medium and cook onion and garlic until soft, stirring occasionally, about 5 minutes. Add tomatoes, ancho chile and half of the tortilla strips. Cook for 5 minutes. Add broth and bring to a boil. Simmer for 15 minutes.
3. Cool slightly. Using an immersion blender or upright blender, puree the mixture until smooth. Return to medium heat, stir in chicken and heat through.
4. To serve, season to taste with lime juice. Garnish with cheese, avocado, cilantro and remaining tortilla strips.