Slice the lemongrass and galangal, remove the stems from kaffir lime leaves, and cut the chicken into bite-sized pieces. Clean and trim the mushrooms. Set everything aside.
Bring water to a gentle simmer. Add the lemongrass, galangal, and kaffir lime leaves. Let the aromatics infuse the broth until fragrant.
Add the sliced chicken to the pot and cook until no longer pink.
Season the soup with tamarind paste, fish sauce, salt, and palm sugar. Stir until everything is well combined and the sugar dissolves.
Add the mushrooms and simmer until just tender.
Pour in the coconut milk and stir gently to combine. Keep the heat low and avoid boiling to prevent the coconut milk from splitting.
Turn off the heat. Add chopped coriander, culantro, green onions, and dried chilies if using. Serve warm.