Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat.
Add diced chicken and cook until browned on all sides, approximately 5 to 7 minutes.
Add onion and bell pepper to the pot and sauté for 4 minutes until softened.
Stir in garlic, Cajun seasoning, cumin, and oregano; cook for 1 minute until fragrant.
Pour in chicken broth, white beans, and green chilies. Bring the mixture to a boil.
Reduce heat to low and simmer uncovered for 15 minutes to allow flavors to meld.
Stir in the cubed cream cheese and heavy cream, whisking gently until the cheese is completely melted and the sauce is smooth.
Simmer for an additional 5 minutes until the chili reaches the desired thickness.
Season with salt and pepper to taste and serve immediately.