Heat the olive oil in a large heavy bottomed pot over medium heat.

Add the diced onion and cook, stirring occasionally, until soft and translucent, about 4 to 5 minutes.

Stir in the garlic, cumin, oregano, cayenne, sea salt, and black pepper and cook until fragrant, about 30 seconds.

Pour in the chicken broth and add the green chiles, scraping up any browned bits from the bottom of the pot.

Bring to a gentle simmer and cook for 10 minutes to let the flavors meld.

Reduce the heat to low and add the softened cream cheese a few cubes at a time, whisking or stirring constantly until fully melted and the broth is smooth.

Stir in the shredded chicken and return the chili to a gentle simmer.

Simmer for 15 to 20 minutes, stirring occasionally, until slightly thickened and the chicken is heated through.

Stir in the heavy cream and simmer for 2 to 3 minutes more.

Taste and adjust seasoning with additional salt, pepper, or cayenne as desired.

If the chili is too thick, add a splash of broth; if it is too thin, simmer uncovered for 5 minutes more until it reaches your preferred consistency.

Ladle into bowls and serve hot with your favorite keto friendly toppings, if desired.