Cut galangal into 1/4 inch slices, and cut lemongrass into 3 inch pieces and bruise them with the back of a knife.
Bring chicken stock, lemongrass, galangal, long pepper, kaffir lime leaves to simmer. Cover and let simmer 15 minutes.
While soup is simmering, heat a small saute pan over medium high heat and add the oil and saute the mushrooms until the are dark brown and crispy. Set aside.
To the soup, add the coconut milk, fish sauce and sugar. return to simmer and remove from the heat.
Spoon into bowls and squeeze with fresh lime juice, add Thai basil and sprinkle with crispy mushrooms and drops of chili oil.