Combine the marinade ingredients mix well. Set aside.
Arrange the chicken in a large resealable bag. Pour the marinade in the bag with the chicken. Gently push the air out of the bag and then seal. Refrigerate overnight.
Combine the ingredients for initial marinade. Set aside.
Combine the final marinade ingredients. Set aside.
Heat-up the grill. Arrange the marinated chicken leg quarters over the grates of the grill. Brush the initial basting sauce on the chicken. Grill in low to medium heat for 7 minutes.
Turn the chicken over. Brush the top part with the initial basting sauce. Grill the other side for another 7 minutes.
Turn the chicken over once more. Baste the top part with initial basting sauce. Continue to grill until the side of the chicken is cooked. Turn it over to completely cook the opposite time. Note that the time will depend on the size of the chicken. The key is to grill in low to medium heat (not high) until the chicken gets fully cooked.
Apply the final basting sauce on both sides of the chicken.
Transfer to a serving plate. Enjoy!