Add the onion, garlic, white beans, green chiles, corn, cumin, oregano, chili powder, salt and pepper to a 6-quart slow cooker. Pour in the chicken broth and stir everything together.
Nestle the chicken breasts into the bean mixture so they are mostly covered by the liquid.
Cover and cook on HIGH for 4 hours or on LOW for 6 to 7 hours, until the chicken is cooked through and shreds easily.
Transfer the chicken to a plate or cutting board and shred it with two forks.
Stir the cream cheese cubes into the hot chili until melted and completely smooth, then stir in the sour cream and lime juice.
Return the shredded chicken to the slow cooker and stir. Let it rest for 5 to 10 minutes to warm through and thicken slightly, then taste, adjust the salt and serve with shredded cheese and your favorite toppings.