Add olive oil to a soup pot or dutch oven on medium-low heat. When the oil is heated, add chopped onion and saute until the onion begins to turn translucent. Then add garlic and cook garlic starts to brown and onion is translucent.
Add oregano, cumin, salt, pepper, paprika, and cayenne pepper (optional) and saute for 1 minute.
Add chicken stock and can of green chiles. Thoroughly stir and turn heat up until mixture reaches a low boil.
Then, reduce the heat to a gentle simmer. Simmer the chili, uncovered, stirring occasionally. Simmer for about 25 minutes until the stock has reduced by at least 1/3.
Turn the heat down to medium. Then add heavy whipping cream, cream cheese, and shredded rotisserie chicken. Cook for 10-15 minutes, stirring occasionally, until chili is fully heated through and cream cheese has fully melted.
Remove from heat and serve topped with cheese, sour cream, etc. as desired.
Notes
You can use a white or yellow onion for the “authentic” color, but I prefer the flavor of red.
To ensure the cream cheese fully melts, either cut it into small pieces before adding it to the soup pot or break it up with a spatula while heating the chili.