Add the chicken, taco seasoning, onion, pepper, garlic, tomatoes, corn, black beans, chiles, and broth to the slow cooker. Mix well to combine, then cover and cook on high for 4 to 5 hours or low for 8 to 7 hours.
Once cooked, transfer the chicken from the slow cooker to a large bowl and shred it with two forks or an electric mixer. Add the shredded chicken back to the slow cooker along with the sour cream and lime juice. Stir to combine. To avoid slight curdling, let the sour cream sit at room temp for 10 to 15 minutes.
To serve, divide evenly among 4 to 6 bowls and top as desired with cilantro, tortilla chips, sour cream, or Greek yogurt.
