Place the bone-in chicken thighs in a large heavy-bottomed pot and add enough water to cover them. Bring to a gentle simmer over medium heat, skimming off any foam that rises to the surface, for about 15 minutes.
Remove the chicken from the broth and set aside to cool slightly. Meanwhile, discard the cooking water or strain it if you prefer a clearer broth. Add a splash of olive oil to the same pot and heat over medium.
Add diced onions, carrots, and celery to the pot and sauté for about 5 minutes, until the vegetables become fragrant and start to soften, filling your kitchen with a savory aroma.
Stir in the minced garlic and thyme, cooking for another minute until the garlic is fragrant and slightly golden.
Pour in the chicken broth, scraping up any browned bits from the bottom of the pot, and bring the mixture to a gentle simmer.
Return the whole chicken thighs to the pot, making sure they are submerged in the broth. Cover and let simmer for about 1.5 hours, skimming foam as needed, until the chicken is cooked through and tender.
Remove the chicken thighs from the soup and let them cool briefly. Shred the meat, discarding the bones and skin, then return the shredded chicken to the pot.
Season the soup with salt and pepper to taste, then let it simmer uncovered for an additional 15 minutes to marry the flavors.
Cut the lemon in half and squeeze fresh lemon juice into the soup, stirring well to brighten the flavors.
Taste and adjust the seasoning if needed, then turn off the heat and let the soup rest for a few minutes.
Serve hot, garnished with additional herbs or lemon slices if desired, and enjoy this comforting, rustic chicken soup.
