Heat a splash of olive oil in a large heavy-bottomed pot over medium heat. Add diced onions, sliced carrots, and chopped celery, stirring occasionally until the vegetables soften and release a fragrant aroma, about 8 minutes.
Push the vegetables to the sides of the pot and add the chicken pieces in the center. Let them sear for a few minutes until lightly browned, then turn to coat with the vegetables.
Pour enough water into the pot to fully cover the chicken and vegetables, then bring to a gentle simmer. Skim off any foam that rises to keep the broth clear and clean.
Add dried thyme and a pinch of salt and pepper. Reduce heat to low, cover partially, and let simmer for at least 1.5 hours, stirring occasionally and skimming foam as needed. The broth will deepen in flavor and become golden.
After simmering, carefully remove the chicken from the pot and shred it into bite-sized pieces using two forks. Return the shredded chicken to the broth.
Taste the broth and adjust seasoning with additional salt and pepper as needed. Let the soup rest for about 10 minutes to let flavors meld.
Just before serving, squeeze a slice of lemon into the soup for brightness and sprinkle chopped parsley on top for freshness.
Serve the soup hot, with a spoonful of shredded chicken, tender vegetables, and a zesty squeeze of lemon to brighten the flavors.
