In a large stock pot or Dutch oven, heat two tablespoons of olive oil or butter over low-medium heat. Add the carrots, celery, and onion. Cook the vegetables for 7 to 8 minutes until they begin to soften and the onions become translucent. Add the garlic and cook for an additional 30 seconds.

Next, add the bay leaves, thyme, salt, pepper, broth, and chicken breast. Bring the soup to a simmer and cook over medium heat for 40 to 50 minutes. Add the potatoes, and continue to cook for an additional 20 minutes or until the potatoes are tender and the chicken can be shredded with a fork.

Remove the chicken breast to a waiting plate and use two forks to shred. Discard the thyme sprigs and bay leaves, then return the shredded chicken to the pot. Stir to combine. Serve hot. Store leftovers in the refrigerator for up to 3 days.