Place the chicken thighs in a large stockpot and add the chopped carrots, celery, and onion around them, then sprinkle with a pinch of salt.
Pour in enough cold water to cover all the ingredients, then bring it to a gentle simmer over medium-low heat, aiming for small bubbles, not vigorous boiling.
Skim off any foam that rises to the surface with a spoon, helping keep the broth clear and clean-tasting.
Let the broth simmer gently for about 1.5 hours, allowing the flavors to deepen and the chicken to become tender and fall apart easily.
Carefully remove the chicken thighs from the broth and set aside to cool slightly.
While the chicken cools, strain the broth through a fine mesh strainer into another pot or bowl, discarding the vegetables and bones, leaving a clear, golden broth.
Shred the cooled chicken meat into bite-sized pieces, removing any skin or bones, and add it back into the strained broth.
Add the thyme sprigs and chopped parsley to the broth, then simmer gently for another 15 minutes to let the flavors meld.
Taste the broth and adjust seasoning with salt and pepper, then squeeze in fresh lemon juice for brightness, stirring well.
Serve the soup hot, garnished with additional chopped parsley and a lemon wedge if desired.
