Place onion, chili beans, black beans, chopped carrot, corn, tomato sauce, diced tomatoes, and beer in a slow cooker. Add taco seasoning and stir to blend. Lay chicken breasts on top of mixture, pressing down slightly until just covered by other ingredients. Cover and cook on Low for 5 hours.
Remove chicken breasts from soup and allow to cool long enough to be handled. Shred chicken and stir back into soup. Continue cooking on Low for 2 hours. Serve with cilantro, Cheddar cheese, light sour cream, and crushed tortilla chips.