In a heavy 5 or 6 quart saucepan, heat the oil over medium-high heat. Sauté the carrots, celery, onion, garlic, 1 teaspoon salt and 1 teaspoon pepper and cook until the onion is translucent, about 5 minutes. Stir in the chicken stock, basil, tomato paste, thyme, and bay leaf. Add the chicken and press down to submerge. Bring the liquid to a simmer. Reduce the heat to medium-low and simmer, uncovered, turning the chicken over and stirring occasionally, for 20 minutes. Add the artichokes and the cannellini beans and simmer until the chicken is cooked through and the liquid has reduced slightly, about 10 to 15 minutes.
Remove the chicken and let cool for 5 minutes. Discard the bones and cut the meat into bite-size pieces. Return the meat to the saucepan and simmer for 5 minutes until warmed through. Remove the bay leaf and discard. Season with salt and pepper, to taste.