Combine the beans, carrots, celery and garlic in a 6- to 8-quart slow cooker. Stir in the tomatoes with their juices and 1 tablespoon olive oil. Add the chicken broth, 1 cup water, the bay leaves, 1/2 teaspoon salt and a few grinds of pepper. Stir well, cover and cook on low until the beans and vegetables are tender, 7 to 8 hours.
Uncover and stir the soup. Cut the corn kernels off the cobs and add to the soup along with the ham. Cover and cook on low until the corn is crisp-tender, about 10 minutes. Stir in the chives and remaining 1 tablespoon olive oil; season with salt and pepper. Discard the bay leaves. Divide among bowls and top with more chives.