How to Make It
In a large saucepan, cover the beans with 2 inches of water and let soak overnight. Drain the beans, return them to the saucepan and add enough water to cover by 2 inches. Bring to a boil over moderate heat and simmer until tender, about 1 hour. Drain the beans.
Meanwhile, put the chicken breasts in a saucepan and add the chicken stock; if necessary, add a little water to cover the chicken. Bring to a simmer and cook over low heat until the chicken is just opaque throughout, about 15 minutes. Transfer the breasts to a plate to cool, then shred. Boil the stock over high heat until reduced to 2 1/2 cups, about 4 minutes.
Heat the oil in a large saucepan. Add the onions and cook over moderate heat, stirring, until translucent, about 4 minutes. Add the canned chiles, garlic, cumin and cayenne and cook, stirring, for 3 minutes. Add the beans, chicken, reduced stock and 4 cups of the cheese and simmer for 10 minutes. Season with salt.
Ladle the chili into large bowls and top each serving with 1/4 cup of cheese and a generous sprinkling of the chopped jalapeños. Serve the sour cream and the remaining cheese and chiles on the side.