Bring the chicken broth to a gentle simmer in a large pot and add the lemongrass, galangal, and kaffir lime leaves, allowing the aromatics to infuse the broth for several minutes.
Pour in the coconut milk and stir gently, then add the sliced chicken and simmer until the chicken is fully cooked and tender.
Add the mushrooms, garlic, fish sauce, and chili, cooking briefly until the mushrooms soften.
Remove from heat, stir in fresh lime juice, discard the lemongrass and galangal, and garnish with fresh cilantro before serving.