Drain the beans. In a large pot, heat the vegetable oil. Add the onions and sauté over med-low heat until translucent (about 5 to 8 minutes). Stir in the garlic, green chilies, cumin, oregano, cloves and cayenne. Sauté for 2 minutes. Add beans and stock. Bring to a boil. Reduce heat and simmer until beans are very tender, stirring occasionally, about 3 to 4 hours.
Grill the chicken and cut chicken into medium dice. Add chicken, beer and 1 cup of cheese to the soup. Serve with remaining cheese, sour cream, salsa and cilantro.