In a large stockpot over medium-high heat, bring 5 cups of water to a boil. Meanwhile, chop the carrots and onion and smash the garlic. Add carrots, celery root, onion, garlic cloves, lemon halves, thyme, parsley stems, bay leaves, salt, and pepper to a boil. Stir. Turn the heat down to medium-heat and allow to cook for about 20 minutes, or until vegetables are tender.
Add the chicken to the pot and reduce the heat to low. Allow to simmer for 25 minutes, or until the chicken registers 160°F. Remove the pot from the heat and allow the chicken to cool in the broth. Once cooled, remove the chicken to a cutting board and shred using two forks or by breaking the chicken apart with your fingers.
In a large bowl, mix mayonnaise, celery, and chopped dill pickles. Add the chicken and fully combine. Add salt and pepper to taste. Serve with crackers, on toasted bread or a croissant, on a bed of lettuce, or just plain!