Heat the oil over medium heat. Add shallots, garlic, ginger, and chiles, and cook until tender, stirring frequently. Add turmeric, cilantro, and sugar and cook, stirring, for another minute. Add lemongrass and 1 cup water.
Add chicken, coat it with sauce, and season with salt and pepper. Turn the heat to low and cover. Cook, turning once or twice, until chicken is cooked through, 10 to 15 minutes. Refrigerate if you're preparing this ahead of time.
Uncover skillet and increase heat to med. high until most of the liquid evaporates. Add the lime zest and fish sauce. Garnish with cilantro.