Stir together broth, green chiles, bell pepper, onion, jalapeño, garlic, cumin, salt, coriander, black pepper, and cayenne pepper in a 6-quart slow cooker until combined. Add chicken in a single layer; cover and cook until chicken is fork-tender and flavors meld, 2 ½ to 3 hours on HIGH or 5 to 6 hours on LOW.
Transfer chicken to a cutting board, and let rest until cool enough to handle, about 5 minutes. Shred meat with 2 forks; discard skin and bones. Set aside.
Mash 1 cup of the beans in a medium bowl with back of a fork or a potato masher until mostly smooth. Add cream cheese and ½ cup of the hot broth mixture; whisk until well combined.
Add cream cheese mixture and reserved shredded chicken to slow cooker. Stir in corn and remaining 2 cups beans. Cover slow cooker, and cook until vegetables are warmed through, about 5 minutes on HIGH or 10 minutes on LOW.
Divide chili evenly among 4 bowls, and garnish with avocado, cilantro, tortilla chips, cheddar, and sour cream.
