Make the Broth: Combine the chicken broth and water in a pot and bring to medium heat. Add the shallots, chilis, galangal, lemongrass, and torn makrut lime leaves to the pot and let simmer for 5-10 minutes.
Cook the Chicken: While the herbs are still simmering, add the chicken breast to the broth and simmer until it is cooked through. Once the chicken is cooked through, remove the pot from the heat.
Remove the Large Herbs: Remove the herbs from the broth, saving the chilis for later plating. Take the chicken out of the broth and allow to cool enough to shred it into bite-sized pieces with a fork.
Season the Soup: Add the shredded chicken and all of the finely sliced herbs (lemongrass, shallots, kaffir lime leaves, cilantro) to the broth. Season with fish sauce and lime juice, tasting and adjusting as needed. Top with reserved chilis and enjoy!