In a large pot or Dutch oven, heat olive oil over medium heat. Add chopped onion and cook until softened, about 5-7 minutes.
Add minced garlic, chili powder, cumin, oregano, and cayenne pepper (if using). Stir and cook for 1 minute until fragrant.
Add the chicken breast to the pot. Pour in the chicken broth. Bring to a boil, then reduce heat, cover, and simmer for 15-20 minutes, or until the chicken is cooked through.
Remove chicken from the pot and shred it with two forks. Return the shredded chicken to the pot.
Stir in the cannellini beans and diced green chilies.
Reduce heat to low. Stir in the heavy cream and shredded Monterey Jack cheese until the cheese is melted and the chili is creamy.
Season with salt and black pepper to taste. Serve hot.
Notes
Garnish with your favorite toppings like avocado, cilantro, or sour cream.