To spatchcock the chicken, cut down either side of the backbone with strong kitchen scissors or poultry shears, then remove the backbone.  (Or ask your butcher to do it for you.)  Turn the chicken over and press down with your hands to flatten the chicken.

Whisk together the olive oil, lemon juice and zest, garlic, oregano, 1½ tsp. salt and ¼ tsp. pepper in a medium bowl. Put the chicken in a gallon-size resealable plastic bag and pour about half of the marinade, reserving the rest to serve with the chicken.  Put the chicken in a rimmed dish (like a pie plate), seal the bag, and smush (technical cooking term) the chicken around in the marinade to evenly distribute it.  Refrigerate the chicken for one hour.

Remove the chicken from the bag and discard the bag with the marinade.  Pat the chicken dry with paper towels and season generously with salt and pepper.  Let sit for 30 minutes at room temperature.

Meanwhile, prepare a grill for indirect heat.  Place the chicken skin side up on the cool side of the grill, with the legs closest to the hot side.  Cover and cook until an instant-read thermometer inserted in the thickest part of the thigh (not touching bone) reads 150°-160°.  This will take about 50 minutes.  Move the chicken to the hot side of the grill and cook for about 2 minutes.  Turn over (skin side down) and grill for about five minutes to crisp the skin.  Retake the temperature; if it is not al least 165°, return the chicken to the cool side of the grill, cover and cook until the temperature is reached.  Remove from the grill, and let rest for 20 minutes before carving.  Add the scallions and dill to the reserved marinade, and pass with the chicken pieces.