Heat olive oil in a large saucepan over medium heat; cook and stir chicken, onion, and garlic into the hot oil until chicken is no longer pink in the center and the juices run clear, 10 to 15 minutes.
Mix Great Northern beans, chicken broth, green chiles, salt, cumin, oregano, black pepper, and cayenne pepper into chicken mixture; bring to a boil. Reduce heat and simmer until flavors have blended, about 30 minutes.
Remove chili from heat; stir in sour cream and whipping cream until incorporated.
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