Sprinkle the chicken on both sides with the Cajun seasoning. Place the chicken in a baking dish and drizzle with the vinegar and oil. Shake the pan gently to coat the chicken underneath. Cover and refrigerate for at least 1 hour or overnight for the best flavor. When you are ready to grill, move the chicken to the counter to take off the chill. Preheat the grill to medium-high heat, about 400 degrees F. Lightly oil the grill and place the chicken on it, smooth-side down. Cook until grill marks appear and the chicken lifts up easily, about 4 minutes. Rotate the chicken by a 45-degree angle and cook to mark, about 3 minutes. Flip the chicken to the other side and cook until cooked through, about 2 minutes. Top with the parsley. Serve hot.
To oil the grill, fold a half sheet of paper towel a few times until it is a small square. Dip one side in oil and, using grill tongs, rub the oiled paper towel on the grill in the areas that you will cook the chicken.
Recipe courtesy of Michelle Dudash