Spray a large Dutch Oven (or similar large pot) with cooking spray, and heat over medium-high heat. Sauté chicken, bell peppers, onions, celery, and garlic for about 5 minutes or until the chicken is almost cooked.
Add the carrots, chili powder, cumin, and coriander. Cook 3-4 more minutes.
Stir in the black beans, crushed tomatoes, diced tomatoes (with their liquid), and beer.
Bring to a boil. Reduce heat to simmer and cook for about 15 minutes, uncovered, stirring frequently. Cook until heated through and carrots are fork tender.
Serve topped with the cheddar cheese, sour cream, chili peppers, and herbs - as desired.