Heat oil in large saucepan over medimum heat until just shimering. Add lemon grass, shallots, cilantro, and 1 tablespoon fish sauce and cook, stirring frequently, until lemon grass and shallots are just softened but not browned, 2 to 5 minutes.
Stir in chicken boroth and 1/2 of coconut milk and bring to a simmer over high heat. Cover, reduce heat to low, and simmer until flavors have blended, about 10 minutes. Pour broth through fine-mesh strainer and discard solids. Rinse saucepan and return broth mixture to pan.
Stir remaining coconut milk and sugar into borth mixture and bring to simmer over medimum high heat, add mushrooms, and cook until just tender, 2 to 3 minutes. Add chicken and cook, stirring constantly, until no longer pink, 1 to 3 minutes. Remove soup from heat. Combine lime juice, curry paste, and remaining 2 tablespoons fish sauce in small bowl and stir into soup.
FOR THE GARNISH: Ladle soup into bowles and garnish with cilantro, chiles, and scallions. Serve immediately with lime wedges.