Combine all the ingredients for the marinade into a food processor and pulse till smooth, reserve one third of a cup.
Place the chicken in a large zip top bag and pour the remaining marinade over top. Remove as much air as possible from the bag and massage the marinade into the chicken and place in the refrigerator for at least 2 hours, but overnight is preferable.
Light your grill and set up for two zone cooking. While the grill is preheating, combine all the ingredients for the Aji Verde sauce into a blender or food processor, and blend until smooth. Set aside.
Place the chicken on the grill over direct heat. Allow the thighs to sear on each side for three minutes. Turn the drumsticks to evenly char them.
Move the chicken over to indirect heat, with the skin side up on the thighs. Close the lid and adjust the temp to maintain 385°F. Allow the chicken to roast till the internal temperature reaches 170°F, then glaze with remaining marinade, close the lid and allow the chicken to finish for ten minutes.
Remove the chicken from the grill and serve with the aji verde sauce.