Sort and wash beans; place in a large Dutch oven. Cover with water 2 inches above beans; let soak 8 hours. Drain beans, and return to Dutch oven. Add 3 cans chicken broth, chopped onion, and next 5 ingredients. Bring to a boil; cover, reduce heat, and simmer 2 hours or until beans are tender.
Add remaining can of chicken broth, chicken, and next 4 ingredients. Bring to a boil; cover, reduce heat, and simmer 1 hour, stirring occasionally. Serve with cheese, salsa, sour cream, and green onions.