Heat oven to 400° F. Season chicken with salt and pepper. Heat a 10-inch skillet over medium-high heat. Once hot, add oil and swirl around pan. Add chicken to pan, skin-side down and cook, undisturbed, until skin is golden brown about 5 minutes, then flip. Cook until golden brown, about 5 more minutes, and then transfer pan to the oven and cook until the chicken reaches an internal temperature of 165° F. Remove the chicken from the pan and set aside to rest for about 2 minutes.
Place the skillet back over a medium heat and add shallot, garlic, and lemongrass. Cook just until they soften, about 10 minutes, and then add soy sauce, fish sauce, and chicken stock. Deglaze the pan, scraping the bottom of the pan with a spoon to release any brown bits. Cook for one minute; remove from the heat. Shred chicken and place in the pan sauce.
Whisk together rice vinegar, salt and sugar in a medium bowl. Once dissolved, add cucumber, carrots, chile, and shallot. Toss to combine; set aside.