Heat the oil in a large heavy bottomed saucepan over medium heat.
Add the celery, carrot, and onion. Saute the vegetables until the onion is translucent, about 5 minutes.
Season with salt and pepper, to taste.
Stir in the tomatoes with their juices, chicken broth, basil, tomato paste, bay leaf, and thyme.
Add the chicken breasts.
Bring the cooking liquid to a boil. 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.
Transfer the chicken breasts to a cutting board and cool for 5 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.
Discard the skin and bones from the chicken breasts.
Shred the chicken into bite- size pieces. Return the chicken meat to the stew. Bring the stew just to a simmer.