Place the chicken pieces in the large pot and pour in cold water, ensuring they are fully submerged. Bring to a gentle simmer over medium heat, and skim off any foam that rises to keep the broth clear.
While the chicken cooks, chop the onion, slice the carrots and celery, and prepare the garlic and thyme.
In a separate pan, heat a splash of olive oil over medium heat and sauté the onions, carrots, and celery until they soften and release a fragrant aroma, about 8 minutes.
Add the minced garlic and chopped thyme to the vegetables; cook for another minute until fragrant.
Remove the chicken from the broth once it’s cooked through and tender, about 45 minutes, then let it cool slightly before shredding into bite-sized pieces.
Strain the broth through a fine sieve into a clean pot, discarding the vegetables and leaving a clear, golden broth.
Add the sautéed vegetables and shredded chicken back into the strained broth. Bring to a gentle simmer for about 10 minutes to meld the flavors.
Season the soup with salt and pepper to taste, then squeeze in fresh lemon juice for a bright, citrusy finish.
Serve the soup hot, garnished with fresh herbs or a drizzle of good olive oil for an added touch of flavor.