
Heat olive oil in a dutch oven over medium heat. Add the onion and saute for 5-7 minutes, until soft.
Add the garlic and saute for 1-2 minutes, until fragrant.
Add the chicken broth, heavy cream, green chiles, cumin, oregano, cayenne pepper, sea salt, and black pepper. Bring to a boil, then lower the heat to medium and simmer for about 40 minutes, until soup has reduced and thickened a bit.
Reduce heat to low. Stir in the cream cheese and shredded cheese, until the cheese has melted and the chicken chili is smooth.
Stir in shredded chicken and simmer for 5 minutes, until thick and creamy.