Season the chicken generously with salt. Place chicken in a glass dish big enough to hold it in a single layer—we used a baking dish. You could also use a zippered plastic bag.

Put 1/3 cup olive oil, lemon zest, lemon juice, garlic, rosemary and a generous grind of black pepper in a measuring cup and whisk with a fork to combine. Pour over chicken in glass dish and turn to evenly coat. Cover the glass dish (we stretched plastic wrap over it) and marinate in the fridge overnight (or at least 4 hours), turning the chicken 2 or 3 times during the process.

About 1/2 hour before you’re ready to put the chicken on the grill, take it out of the fridge and let it come to room temperature. If you’re grilling with charcoal, do this when you light the coals.

Arrange the grill for indirect cooking; again, if you’re using charcoal, arrange the coals on one side of the grill. Lightly brush the grilling rack with oil. Remove the chicken from the marinade, shaking off excess marinade, and place it on the grill skin side down away from the coals. Close the lid and cook for 5 minutes. Turn the chicken, close the lid and cook for another 5 minutes.

Move the chicken over the coals or heat, skin side down. Close the lid and cook for 5 minutes. Turn the chicken skin side up; if some pieces are getting charred, swap them around to cooler spots (like where the less charred pieces were). Close the lid and cook for another 5 minutes.

By now, if the chicken’s not done, it should be getting close. Check with an instant read thermometer. If it’s at least 165ºF in the thickest parts, it’s done. If not, move it to the indirect cooking part of the grill, close the lid and continue to cook, checking every 4 minutes or so.

While the chicken is grilling, place the lemon halves cut side down over the coals. You want them to get a little charred and take on some smoke. Transfer them to a bowl and set aside.

When it’s done, transfer chicken to a platter and let it rest for 5 minutes. Squeeze the grilled lemon halves over the chicken, then serve.