1. Make tortilla strips: Preheat oven to 375°F. Stack tortillas and cut into 1/4-inch strips. Toss in a bowl with vegetable oil, 1/2 tsp. salt and a pinch of pepper. Spread in a single layer on a large baking sheet. Bake for 10 to 12 minutes, until golden and crisp, rotating pan halfway through. (Tortillas can be prepared up to 5 days in advance. Keep tightly covered in a cool, dark place.)
2. Make soup: Warm olive oil in a large pot over medium-high heat. Add onion, celery, carrots and jalapeño and cook, stirring often, until softened but not browned, about 5 minutes. Sprinkle chili powder and cornmeal over vegetables and cook for 1 minute, stirring constantly to prevent scorching. Pour in broth, scraping bottom of pot. Bring to a boil over high heat. Reduce heat to medium-low, add chicken; simmer, partially covered, until chicken is very tender, 30 minutes.
3. Transfer chicken to a work surface; let rest until cool enough to handle, about 15 minutes. Turn off heat under soup and skim off fat. Shred chicken and discard skin, bones and gristle. Return shredded chicken to pot along with beans. Cook over medium heat, stirring occasionally, until warmed through, about 5 minutes. Season with additional salt and pepper, if desired. (Can be made up to 2 days in advance to this point. Cover and chill.) Stir in cilantro just before serving.
4. Serve soup hot, garnished with tortilla strips, avocado and lime wedges.