Preheat the grill to medium-high (400 degrees F) and lightly oil the grates.

Make the herb butter by combining softened butter with the oregano, zest, salt and pepper.

Separate the skin from the breast meat of the chicken by gently sliding your fingers between the two. Fill this area with half of the butter, then spread the rest over the skin on the outside.

Place the chicken over indirect heat (eg the burners directly below the chicken should be turned off, while the outer burners surrounding it should remain on.

Cover and cook for 45 minutes to 1 hour or until the chicken's internal temperature reaches 165F  - use a meat thermometer to check. Rotate the chicken as needed to obtain even coloring. 

Let rest for 10 minutes before carving.