Heat the large soup pot over medium heat, then add chopped onions, minced garlic, and sliced ginger. Sauté for about 5 minutes, until fragrant and the onions are translucent.
Add the sliced carrots and celery to the pot, cooking for another 5 minutes until they start to soften and release their aroma, stirring occasionally.
Pour in the chicken stock, bringing the mixture to a gentle simmer. Toss in the bruised lemongrass stalks and a splash of fish sauce to deepen the flavor.
Once bubbling, add the diced chicken breasts to the broth. Cook for about 8-10 minutes until the chicken is just cooked through and tender, skimming off any foam.
Remove the lemongrass stalks from the soup and discard or set aside for another use. Taste the broth and adjust seasoning with salt, pepper, or more fish sauce if needed.
Squeeze fresh lime juice into the soup to brighten the flavors, stirring gently to combine.
Serve the hot soup in bowls, garnished with additional lime wedges or herbs if desired, for a fresh finishing touch.