**Sauté Aromatics:** Heat olive oil in a large pot over medium heat. Add diced onion and garlic, cooking until softened and fragrant, about 2–3 minutes.
**Cook Chicken:** Add the chicken breasts or thighs to the pot. Pour in chicken broth and bring to a boil. Reduce heat to a simmer, cover, and cook for 15–20 minutes, or until the chicken is fully cooked and tender.
**Shred Chicken:** Remove the chicken from the pot and shred it using two forks. Return the shredded chicken to the pot.
**Add Beans and Spices:** Stir in the cannellini beans, great northern beans, diced green chilies, cumin, chili powder, paprika, oregano, cayenne pepper (if using), salt, and black pepper. Simmer for an additional 10 minutes to allow the flavors to meld.
**Make It Creamy:** Reduce the heat to low. Stir in sour cream and heavy cream, mixing until well combined. Add lime juice and adjust seasoning as needed.
**Serve:** Ladle the chili into bowls and garnish with fresh cilantro. For extra indulgence, top with shredded cheese and serve with tortilla chips.