Heat the oil in a large saucepan over medium heat. Slowly cook and stir the onion until tender. Mix in the garlic, jalapeno, green chile peppers, cumin, oregano and cayenne. Continue to cook and stir the mixture until tender, about 3 minutes. Mix in the chicken broth, chicken and white beans. Bring to a boil. Turn down heat and simmer 15 minutes, stirring occasionally.
Remove the mixture from heat. Slowly stir in the cheese until melted. Serve warm. (I usually put the cheese into each bowl individually, not into the pot).