1) Heat the oil in a heavy 5 1/2-litre saucepan over medium heat. Add the celery, carrot and onion. Saute the vegetables until the onion is translucent, about five minutes. Season with salt and pepper, to taste. Stir in the tomatoes with their juices, chicken stock, basil, tomato puree, bay leaf and thyme. Add the chicken breasts; press to submerge.
2) Bring the cooking liquid to a simmer. Reduce the heat to medium-low and simmer gently, uncovered, until the chicken is almost cooked through, turning the chicken breasts over and stirring the mixture occasionally, about 25 minutes. Using tongs, transfer the chicken breasts to a work surface and cool for five minutes. Discard the bay leaf. Add the kidney beans to the pot and simmer until the liquid has reduced into a stew consistency, about 10 minutes.
3) Discard the skin and bones from the chicken breasts. Shred or cut the chicken into bite-sized pieces. Return the chicken meat to the stew. Bring the stew just to a simmer. Season with salt and pepper, to taste.
Ladle the stew into serving bowls and serve with the bread.