In a large bowl, combine oil, fish sauce, lime juice, lemongrass, cilantro, garlic, sugar, salt and pepper. Stir to combine. Add the chicken and toss to thoroughly coat. Cover and refrigerate at least 1 hour up to overnight.
Heat a grill to 400 degrees. Chop chicken into 2-inch pieces and place on soaked bamboo skewers, approximately 3 to 4 pieces per skewer. Grill each side until cooked and the chicken reaches an internal temperature of 165 degrees.