In a large pot, boil chicken in water until cooked through. Remove and chop into bite-sized pieces. Set aside.
Heat olive oil in the same large pot. Add onion and cook 4–5 minutes, until translucent.
Add garlic, salt, oregano, cumin, and black pepper. Cook one minute, until fragrant.
Add green chiles, chicken broth, chicken, and beans.
Simmer for 30 minutes.
Whisk heavy cream and cornstarch together in a small bowl.
Remove chili from heat. Stir in the cream mixture and sour cream until smooth and thickened.
Serve with your favorite toppings.