Rinse beans. Place in a 5- to 6-quart Dutch oven and add the water. Bring to boiling; reduce heat. Simmer, uncovered, for 2 minutes. Remove from heat. Cover and let stand for 1 hour. (Or place beans in water in Dutch oven. Cover and let soak in a cool place for 6 to 8 hours or overnight.) Drain and rinse beans; set aside.
In same Dutch oven, stir together the drained beans, chicken broth, onion, garlic, canned chile peppers, oregano, cumin, cayenne pepper and black pepper. Bring to boiling; reduce heat. Simmer, covered, for 1 1/2 hours.
Stir in the chicken. Simmer, covered, for 30 minutes more. Just before serving, stir in the 1/2 cup cheese until just melted. If you like, serve with fresh chile peppers and/or additional cheese.