Place beans in large heavy pot. Add enough cold water to cover; soak overnight.
Place chicken in large heavy saucepan. Add cold water to cover, and bring to a simmer. Cook until tender. Drain and reserve broth; cool. Cut chicken into cubes, and set aside. Drain beans.
Heat oil in same pot over medium-high heat. Add onions and sauté until translucent, about 10 minutes. Stir in garlic, chiles, cumin, oregano, cloves, and cayenne; sauté 2 minutes.
Add beans and reserved broth; bring to a boil. Reduce heat and simmer until beans are very tender, about 2 hours, stirring occasionally. Add chicken and 1 cup cheese to chili and stir until cheese melts. Season to taste with salt and pepper. Ladle chili into bowls. Serve with remaining cheese, sour cream, and salsa.
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