Heat the oil in a large saucepan over medium heat.
When the oil is warm, add the onion, and cook for 5 minutes. Add the garlic to the pan, and cook for another minute.
Add the chicken, broth, green chilis, oregano, chili powder, salt, and cayenne pepper to the pan.
Cover and reduce heat to a simmer. Cook for 20 minutes. Remove the chicken from the saucepan, and shred it with forks.
Add the cubed cream cheese to the liquid.
Cook, over low heat, until the cheese melts, about 4 minutes.
Return the chicken to the pot, and cook for another 5 to 7 minutes to allow the flavors to combine.
Stir in the fresh lime juice.
Serve warm with sour cream, cheese, lime wedges, jalapeños, and cilantro.