Place chicken in the bottom of a 6-quart or larger slow cooker. Top with chicken broth, white beans, green chiles, garlic, onion, cumin, oregano, salt, and cayenne. Stir to combine.

Cover and cook on low for 4 to 6 hours or high for 2 to 4 hours, until chicken is cooked through.

Remove chicken breasts to a plate. Once cool enough to handle, shred and set aside.

With an immersion blender, puree a portion of the chili to thicken it, leaving some of the beans whole. Alternatively, transfer a few ladlefuls to a food processor or blender and pulse roughly, then return to the chili.

Stir in shredded chicken and cilantro. Portion into bowls and top with fresh lime juice. Add any other desired toppings and enjoy.