Place diced tomatoes, chili beans, black beans, corn, beer, tomato sauce, and onion into a slow cooker. Add taco seasoning; stir to blend. Lay chicken breasts on top, pressing down slightly until just covered.
Cover and cook on Low for 5 hours.
Transfer chicken breasts to a chopping board and allow to cool long enough to be handled; shred chicken with two forks and add back into soup. Cover and continue cooking for 2 hours.
Serve in bowls topped with shredded Cheddar cheese, a dollop of sour cream, and crushed tortilla chips.