Heat the oil in a heavy 5 1/2 saucepan over medium heat.
Add the celery, carrot, and onion
Sauté 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, and press to submerge.
Bring the cooking liquid to a simmer
Reduce the heat to medium to low and simmer gently, uncovered, until the chicken is almost cooked through, turning the chicken breasts over and stirring the mixture occasionally (for about 25 minutes).
Using tongs, transfer the chicken breasts to a work surface and cool for 5 minutes. Discard the bay leaf.
Add the kidney beans to the pot and simmer until the liquid has reduced to a stew consistency (takes about ten minutes).
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 to a simmer and season with salt and pepper to taste.
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