Heat olive oil in a large pot or Dutch oven over medium heat. Add onion and cook until softened, about 5 minutes. Add garlic and cook for another minute until fragrant.
Stir in the cooked and shredded chicken, cannellini beans, great northern beans, corn, and green chiles.
Pour in the chicken broth. Add cumin, oregano, cayenne pepper (if using), salt, and black pepper. Stir to combine.
Bring the chili to a simmer, then reduce heat to low, cover, and cook for at least 20 minutes to allow the flavors to meld.
If desired, stir in the heavy cream just before serving for a creamier texture.
Serve hot with your favorite toppings.
Notes
For a spicier chili, add more cayenne pepper or a pinch of red pepper flakes.
You can use leftover rotisserie chicken for a quicker preparation.