Begin by preparing all necessary ingredients.
In a large saucepan, heat olive oil over medium heat. Add the diced chicken, chopped onion, and minced garlic. Stir and cook until the chicken is fully cooked, with no pink remaining and the juices run clear, approximately 10 to 15 minutes.
Mix in the drained beans, chicken broth, chopped green chiles, salt, cumin, oregano, black pepper, and cayenne pepper. Bring the mixture to a boil, then reduce the heat and allow it to simmer for around 30 minutes, enabling the flavors to meld together.
Remove the saucepan from the heat and blend in the sour cream and heavy whipping cream until fully incorporated and smooth.
Serve the chili while it's hot and enjoy the delightful creaminess of each bite.