Rinse the chicken under cold water and remove any giblets.
Place the chicken in a large pot and cover it with water.
Bring the water to a boil, then reduce to a simmer.
Skim off any foam that forms on the surface.
Add the chopped onion, garlic, carrots, and celery to the pot.
Season with thyme, salt, and pepper.
Cover and let it simmer for about 40-50 minutes, until the chicken is cooked through.
Carefully remove the chicken from the pot and let it cool slightly.
Shred the chicken meat, discarding the skin and bones.
Return the shredded chicken to the pot, stir well, and simmer for another 10 minutes.