Heat the large pot over medium heat and add a splash of olive oil. Once shimmering, place the chicken pieces in the pot and brown them until golden on all sides, about 8 minutes. Remove the chicken and set aside.
Add the diced onion, chopped carrots, and celery to the same pot. Sauté the vegetables until they become fragrant and slightly softened, about 5 minutes, listening for a gentle sizzle and watching for the vegetables to turn tender.
Pour in water or chicken broth, then return the browned chicken to the pot. Bring the mixture to a gentle simmer, skimming off any foam that rises to the top. Cover partially and let it simmer for about 45 minutes, until the chicken is cooked through and tender.
Remove the chicken from the pot, let it cool slightly, then shred the meat into bite-sized pieces. Return the shredded chicken to the soup, stirring to combine.
Add lemon zest and chopped herbs (parsley and thyme) to the soup. Stir well and let it simmer for another 10 minutes, allowing flavors to meld and the broth to brighten.
Stir in lemon juice and taste the soup. Adjust seasoning with salt and pepper as needed, then cook for another 2-3 minutes to incorporate the flavors fully.
Serve the soup hot, ladled into bowls, with an extra sprinkle of fresh herbs and a drizzle of olive oil if desired. Enjoy the vibrant, comforting flavors with a slice of crusty bread.
