In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion and cook for 3–4 minutes, until softened. Stir in the garlic and cook for another minute.
Stir in cumin, chili powder, oregano, salt, and pepper. Add the green chiles and cook for 1–2 minutes to release their flavor.
Add the white beans, shredded chicken, and chicken broth. Bring to a gentle boil, then reduce the heat and let simmer for 15–20 minutes to meld the flavors.
Stir in the sour cream and half and half, mixing until fully combined. Simmer for another 5 minutes until heated through and creamy. Add lime juice, if using, for a bright finish.
Ladle the chili into bowls and top with fresh cilantro, shredded cheese, tortilla chips, or avocado.