Place the butter in a large saucepan or pot on the stovetop over medium heat.
Add the onion, celery, and bell pepper to the saucepan and sauté until just starting to become tender.
Add the jalapeño to the saucepan and sauté for another 2-3 minutes.
Mix in the shredded chicken, cream cheese, sour cream, cumin, oregano, and salt and pepper to taste until the cream cheese has melted and the mixture is combined.
Whisk the chicken broth into the pot, then cover and simmer for 10 minutes.
Stir the heavy whipping cream into the soup and simmer another 5 minutes, uncovered, before serving.