Place the chicken breasts in the bottom of the slow cooker.
Add the drained white beans, diced green chiles, and chopped onion on top of the chicken.
Pour in the chicken broth. Sprinkle the cumin, chili powder, oregano, salt, and black pepper over everything.
Stir gently to combine the ingredients.
Cover and cook on low for 6 to 8 hours.
Remove the chicken breasts and shred them with two forks. Return the shredded chicken to the pot and stir to mix it through the chili.
Ladle into bowls and add shredded cheese, sour cream, and cilantro as desired.