Heat oil in large pot over medium high heat, add onions and saut� until translucent, about 10 minutes.
Stir in garlic, then chilies, cumin, oregano, and cayenne and saut� 2 minutes. Add undrained beans and broth and bring to a boil.
Reduce heat and add chicken and cheese to chili and stir until cheese melts.
Season to taste with salt and pepper and ladle into bowls.