Gather all ingredients and prepare by chopping carrots, celery, and onion into small, uniform pieces.
Heat a large heavy-bottomed pot over medium heat and add a tablespoon of oil. Sauté the chopped vegetables until they soften and release a sweet aroma, about 5 minutes.
Add the bone-in chicken to the pot and cover with cold water. Bring to a gentle simmer, just below boiling point, and skim off any foam that rises to the top.
Reduce heat to low and let the broth simmer gently for 45 minutes, until the chicken is cooked through and tender.
Remove the chicken from the broth, let it cool slightly, then shred the meat with two forks. Return the shredded chicken to the pot.
Add bruised lemongrass stalks and a splash of fish sauce to the broth, then simmer for another 10 minutes to let the flavors meld.
Toss in chopped fresh herbs like cilantro and Thai basil, stirring gently to release their aromatic oils.
Taste the broth and adjust seasoning if needed with additional fish sauce, salt, or pepper.
Serve the hot soup in bowls, garnished with extra herbs and a squeeze of lime for bright, fresh flavor.