2. Cook the bacon in a 4-quart pot over low-medium heat for 2 to 3 minutes. Add the onion, celery, green pepper and jalapeño pepper, season lightly with black pepper and cook until the vegetables begin to soften, about 5 minutes. Add the garlic and cook for 1 more minute.
3. Add the bay leaf, cilantro stems, beans and broth and bring to a boil quickly over high heat.
4. Lower the heat and simmer until the beans are completely tender, about 30 to 40 minutes.
5. Remove and discard the bay leaf, puree half of the soup in a blender and then add it to the rest of the soup. Season with salt and pepper and keep warm.
6. Remove and discard the skin and fat from the chicken breasts. Cut the meat into 1/2" cubes.
7. Divide the chicken among the soup bowls, mounding it in the center, and ladle the soup around it. Garnish with chopped cilantro.
NOTE: Do not add salt until the beans are fully cooked because salt will prevent them from becoming tender.