Gather all your ingredients and prep your vegetables by dicing the onion, slicing the carrots and celery.
In a large stockpot, heat the olive oil or butter over medium heat until it shimmers and begins to smell fragrant.
Add the chicken pieces to the pot and sear them until golden on each side, about 5 minutes per side, hearing a satisfying sizzle.
Remove the chicken and set aside briefly. In the same pot, add diced onion, sliced carrots, and celery, sautéing until fragrant and slightly caramelized, about 10 minutes.
Pour in the water or broth, bringing the mixture to a gentle boil, and then add the seared chicken back into the pot.
Reduce the heat to low and let the soup simmer gently, uncovered, for about 1 hour, occasionally skimming foam from the surface.
Check the chicken for doneness; it should be tender and easy to shred. Remove the chicken and shred it with two forks.
Return the shredded chicken to the pot, squeeze in fresh lemon juice, and stir in chopped parsley and thyme for brightness and freshness.
Season the soup with salt and pepper to taste, then let it rest for 10 minutes to allow flavors to meld.
Ladle the hot soup into bowls, garnish with additional parsley if desired, and serve with crusty bread for a complete meal.