In a large saucepan over medium-low heat add oil. Add onions and stir fry until tender. Mix in garlic, green chilies, cumin, oregano, and cayenne pepper. Continue to stir fry for about 3 minutes.
Mix in chicken broth, chicken and white beans. Simmer for 15 minutes, stirring occasionally.
Remove from heat and slowly stir in the shredded cheese until melted. Serve warm