Trim the chicken of any excess fat and skin, leaving the majority of the skin on the chicken. This will help keep the chicken juicy and flavorful. Drizzle the chicken with the olive oil.
Place the chicken skin-side down and cook for 10 minutes with the grill lid closed.
To make sure the chicken is properly cooked through, use an instant read digital meat thermometer. Internal temp needs to reach 165 degrees.
Once the chicken quarters come off the grill, let them rest about 10 minutes before serving. This will keep the chicken extra juicy! Serve with the reserved sauce.