In a stockpot, add the chicken, stock, salt and enough water to cover by 1 inch. Bring to a boil; skim. Lower the heat and add the onions, carrots, celery, garlic, thyme and peppercorns. Partially cover and simmer until the vegetables are tender and the chicken is cooked, about 1 hour.
Transfer the chicken to a cutting board; let cool, then shred (discard the bones). Transfer the carrots and half of the celery and onions to a bowl, then dice into bite-size pieces.
Strain the broth through a sieve into a bowl, pressing down to extract any juices; discard the solids. Skim the surface of the broth and discard any fat. Return the chicken and vegetables to the pot, add the broth and reheat over medium heat until simmering.