Heat olive oil in a large heavy-bottomed pot over medium heat until shimmering and fragrant.
Add chopped onions, carrots, and celery to the pot. Sauté, stirring occasionally, until the vegetables are soft and fragrant, about 8 minutes, and they begin to develop a slight golden color.
Place the chicken thighs into the pot, skin-side down if using skinless, and brown each side for about 5 minutes, until golden brown and slightly crispy.
Pour in the chicken broth, add the sprig of rosemary, and bring the mixture to a gentle simmer. Cover the pot partially and cook for 20 minutes, allowing the flavors to meld and the chicken to become tender.
Remove the chicken thighs from the pot, shred the meat using two forks, discarding the bones if bone-in, and return the shredded chicken to the soup.
Add freshly squeezed lemon juice to brighten the broth, then season generously with salt and pepper, tasting and adjusting as needed.
Let the soup simmer uncovered for an additional 10 minutes to let the flavors deepen and the broth slightly thicken.
Stir in chopped parsley for a fresh herbal note and drizzle a little extra olive oil over each bowl before serving.
Serve hot, garnished with parsley and a slice of lemon if desired, and enjoy this comforting, vibrant chicken soup.
