Chop the onion, carrots, and celery into small, uniform pieces for even cooking.
Heat a large pot over medium heat and add olive oil, allowing it to warm until shimmering and fragrant.
Sauté the diced onion, sliced carrots, and chopped celery in the hot oil until they soften slightly and become fragrant, about 5 minutes.
Place the chicken breasts into the pot and cover with water or broth, ensuring they are fully submerged.
Bring the mixture to a gentle simmer, then reduce heat to low and cook uncovered for 30-40 minutes, skimming off foam as needed, until the chicken is cooked through and broth is flavorful.
Remove the cooked chicken breasts from the pot and place on a cutting board to cool slightly, then shred into bite-sized pieces.
Return the shredded chicken to the pot, stir in the dried thyme and half of the chopped parsley.
Simmer the soup for another 10 minutes to allow flavors to meld, then season with salt and pepper to taste.
Cut the lemon in half and squeeze the juice into the soup, stirring well to brighten the flavors.
Taste the broth and adjust the seasoning if needed, adding more salt, pepper, or lemon juice for extra brightness.
Garnish the soup with remaining chopped parsley and serve hot in bowls, enjoying the vibrant, clear broth with tender chicken and fresh herbs.
