Place the chicken breasts in the bottom of your slow cooker. Add the Great Northern beans, green chiles, diced onion, and minced garlic.
Pour the chicken broth over everything, then add the cumin, oregano, cayenne pepper (if using), salt, and black pepper. Stir gently to combine.
Cover and cook on LOW for 4-6 hours or on HIGH for 2-3 hours, until the chicken is cooked through and tender.
Remove the chicken from the slow cooker and shred it using two forks. Return the shredded chicken to the slow cooker.
Add the cubed cream cheese and shredded Monterey Jack cheese. Stir until the cheeses are completely melted and the chili is creamy, about 5-10 minutes.
Serve hot with tortilla chips, fresh cilantro, lime wedges, and sliced avocado on top. Absolutely delicious!