In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion and cook until translucent, about 3–4 minutes. Stir in the garlic and green chiles, and cook for another minute.
Add the shredded chicken, white beans, cumin, oregano, chili powder, salt, and pepper. Stir to combine and coat everything with the spices.
Pour in the chicken broth and bring the mixture to a gentle boil. Reduce heat and simmer uncovered for about 15–20 minutes, stirring occasionally.
Reduce the heat to low. Stir in the sour cream and heavy cream, mixing until fully incorporated and warmed through. Do not boil after adding the dairy.
Ladle the chili into bowls and top with your favorite garnishes. Serve with tortilla chips or crusty bread.