Pour the coconut milk and chicken stock into a large pot set over medium heat. Stir until well combined and allow it to reach a gentle simmer.
Add the lemongrass, kaffir lime leaves, galangal, and bird chilies into the pot, letting the flavors meld together for about 10 minutes.
Add the thinly sliced chicken and mushrooms, cooking until the chicken is tender and fully cooked, about 5 to 7 minutes.
Incorporate the sliced onion, fish sauce, lime juice, and sugar, allowing the soup to simmer for an additional 2 to 3 minutes.
Taste the soup and modify the seasoning with extra fish sauce or lime juice as needed.
Remove the pot from heat and discard the lemongrass and lime leaves.
Serve the soup hot, garnished with fresh cilantro and lime wedges on the side.