In a large pan heat oil. Add chicken and onion. Saute, stirring occasionally, until chicken is no longer pink and onion is tender.
Add broth, green chilies, and seasonings.
Bring to a boil. Reduce heat to low.
Simmer for 20-25 minutes. Stirring occasionally.
Remove from heat. Stir in sour cream and milk. (Make sure the soup is not boiling or it will break down and separate the dairy.)
Stir in cheese or serve with cheese sprinkled on top.
