Place the chicken breasts in the bottom of the slow cooker. Add the diced onion, minced garlic, drained white beans, and diced green chiles.
Pour in the chicken broth. Sprinkle the cumin, oregano, chili powder, salt, and black pepper over the top. Stir gently to combine.
Cover and cook on low for 6 hours or until the chicken is fully cooked and easy to shred.
Remove the chicken breasts and shred them with two forks. Return the shredded chicken to the slow cooker.
Add the cubed cream cheese. Stir until the cream cheese melts and the chili turns creamy. Taste and adjust salt or pepper if needed.
Ladle into bowls and top with chopped cilantro, shredded Monterey Jack cheese, and a squeeze of lime.