Chop the onion, carrots, and celery into uniform pieces for even cooking, and set aside.
Heat a large pot over medium heat and add olive oil. Sauté the chopped onion, carrots, and celery until they become fragrant and slightly tender, about 5 minutes, filling the kitchen with a savory aroma.
Add the chicken breast to the pot, then pour in water to cover the ingredients. Bring to a gentle simmer over medium heat, skimming off any foam that rises to the surface.
Reduce the heat to low and let the soup simmer gently for 30 to 40 minutes, until the chicken is cooked through and the broth is flavorful. The aroma should be rich, and the liquid slightly golden.
Remove the chicken from the broth and set aside to cool slightly. Shred the chicken into fine pieces using two forks or your hands.
Return the shredded chicken to the pot, then stir in chopped thyme and season with salt and pepper to taste. Let it cook for another 10 minutes to meld the flavors and warm through.
Cut the lemon in half and squeeze fresh lemon juice into the soup, stirring well. The bright citrus will lift the flavors instantly.
Taste the broth and adjust seasoning, adding more salt, pepper, or lemon if desired. The broth should be clear, golden, and fragrant with herbs and lemon.
Ladle the hot soup into bowls, garnish with chopped parsley, and serve immediately for a comforting, bright meal.