Heat the oil in a large pot over medium heat. Add the onions and garlic and saute for 10 minutes, or until onions are tender. Add the chicken, chicken broth, green chile peppers, cumin, oregano and cayenne pepper and bring to a boil.
Reduce heat to low and add the beans. Simmer for 20 to 30 minutes, or until heated thoroughly. Pour into individual bowls and top with the cheese.