In a large pot, warm the butter or olive oil over medium heat. Add the chopped onion and bell pepper, sautéing for 3 to 5 minutes until softened. Then, mix in the minced garlic and cook for an additional 2 to 3 minutes.
Incorporate the ground chicken, cooking until fully done, about 10 minutes, breaking it apart as needed.
Add cumin, chili powder, oregano, salt, and pepper, stirring well.
Mix in the green chiles, followed by the chicken broth and heavy cream.
Introduce the cream cheese blocks, simmering until melted and blended into the chili, about 10 to 15 minutes, stirring occasionally.
Squeeze in lime juice, reduce heat, and let simmer for at least 15 more minutes to enhance flavors.
Serve with lime wedges, fresh cilantro, and shredded cheese if desired. Enjoy!