On a work surface, with a sharp knife or kitchen shears, cut along one side of the backbone of the chicken. Open the chicken and spread it out flat. Gently lift the skin from the breast and legs, without tearing it, to allow the marinade to seep into the meat. Set aside.
In a large glass dish or large sealable plastic bag, combine all the ingredients. Add the chicken, thoroughly coating it with the marinade. Cover the dish or seal the bag and refrigerate
for 1 to 24 hours.
Preheat one side of the grill, setting the burner to high.
Oil the grate of the unheated side of the grill.
Lay the chicken flat on the unheated side of the barbecue, skin side down. Close the lid.
Cook for 45 minutes. Turn the chicken and continue cooking for about 35 minutes or until a thermometer inserted in the thigh, without touching the bone, reads 180°F (82°C).
In a bowl, combine all the ingredients. Season with salt
Serve the chicken with the pesto mayonnaise and your choice of grilled vegetables.