Heat olive oil in a large pot or Dutch oven over medium-high heat. Add chicken and cook until browned on all sides. Remove chicken from pot and set aside.
Add onion to the pot and cook until softened, about 5 minutes. Add garlic, cumin, oregano, salt, and pepper, and cook for 1 minute more until fragrant.
Stir in the cannellini beans and diced green chiles.
Pour in the chicken broth and bring to a simmer. Return the chicken to the pot.
Reduce heat to low, cover, and simmer for at least 20 minutes, or until the chicken is cooked through and the flavors have melded.
Stir in the shredded Monterey Jack cheese until melted.
Serve hot, with your favorite toppings.
Notes
For a spicier chili, add a pinch of cayenne pepper or a chopped jalapeño with the onions.
If you prefer a thicker chili, you can mash some of the beans against the side of the pot before serving.
Leftovers can be stored in an airtight container in the refrigerator for up to 3 days.