Heat the grill to medium.
Brush the chicken and potatoes with oil and season with salt and pepper. Place the chicken on the grill, skin-side down and grill until golden brown and slightly charred, 6 to 7 minutes. Turn the chicken over and continue grilling until just cooked through, 5 to 6 minutes. A few minutes before the chicken has finished cooking, place the potatoes on the grill, cut-side down and cook until lightly golden brown, about 2 minutes. Turn over and continue grilling about a minute longer. Remove the chicken and potatoes to a platter and immediately drizzle with the roasted garlic-oregano vinaigrette. Let rest 5 minutes before serving. Garnish with oregano sprigs and parsley sprigs.