Layer the base. Add beans, green chiles, onion, and garlic to the slow cooker.
Pour in the chicken broth. Sprinkle in cumin, chili powder, oregano, coriander, salt, pepper, and cayenne if using. Stir to combine.
Add the chicken. Nestle the chicken breasts or thighs into the mixture so they’re submerged.
Cover with the lid.
Cook low and slow. Cook on Low for 6–7 hours or High for 3–4 hours, until the chicken is cooked through and easily shreds.
Shred the chicken. Transfer the chicken to a cutting board and shred with two forks. Return the chicken to the slow cooker.
Make it creamy. Add the cream cheese and sour cream. Stir until the cream cheese melts and the chili turns velvety.
If needed, cover and let it warm for another 10–15 minutes, stirring once or twice.
Brighten the flavor. Stir in the lime juice. Taste and adjust seasoning with extra salt, pepper, or lime as needed.
Serve and garnish. Ladle into bowls and top with cheese, cilantro, jalapeños, avocado, green onions, or crushed tortilla chips. Serve with lime wedges.