Place chicken in the bottom of a 6-quart or larger slow cooker (I use this one
). 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.