Place chicken in bottom of a 6-quart or larger slow cooker. Top with the 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 the chicken is cooked through. Remove the 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. (You can also transfer a few ladlefuls of the chili to a food processor and roughly blend, then stir the blended portion back into the chili). Stir in the shredded chicken and cilantro. Portion into bowls and top with a squeeze of fresh lime juice. Add any other desired toppings and enjoy. Makes 6 servings.
Per serving (without toppings) : Calories 315, carbs 36g, protein 34g, fat 4g, sat fat 1g, chol 60mg, fiber 8g, sugar 2g