Add the beans to a large container and cover them with water. Let sit overnight. To speed this process up, boil the water and cover the beans, and let sit for 1 hour. Drain before using it.
Next, season the chicken breasts on all sides with salt and pepper. Add the oil to a large pot over medium heat and sear the chicken breasts on both sides, and cooked throughout.
Set the chicken to the side and add the onions, carrots, celery, garlic, mushrooms, and squash to the pot and sauté for 8 to 10 minutes or until light brown.
Add the chicken back in, along with the drained beans and chicken stock. Cook over low heat for 60 to 90 minutes or until the chicken pulls apart easily.