Heat the vegetable oil in a large pot over medium heat.
Add the chicken broth and bring it to a gentle simmer.
Stir in the coconut milk, followed by the sliced chicken breast. Cook for about 10 minutes or until the chicken is cooked through.
Add the sliced mushrooms, lemongrass, kaffir lime leaves, galangal, and bird chilies to the pot. Continue simmering for another 5-10 minutes until the mushrooms soften.
Season the soup with fish sauce and lime juice, tasting for balance. Adjust seasoning as needed.
Remove the pot from heat and discard lemongrass, lime leaves, and galangal pieces (if desired).
Serve hot, garnished with fresh cilantro and sliced green onions if using.