Purée onion, garlic, herbs, oil and zest in a food processor.
Rub some purée under skin of chicken breast. Rub remaining purée over rest of bird. Refrigerate at least 6 hours and up to 8 hours. Let stand at room temperature 30 minutes. Wipe off most of rub; season with salt and pepper.
Heat grill to medium-high, or set up for indirect heat. Grill chicken, breast side down, covered with vent open, until nicely charred, 10 to 15 minutes. Flip; cook 30 minutes more. Flip again; grill until internal temperature reaches 165 degrees in thickest part of breast, 5 minutes more. Let rest 10 minutes.
To spatchcock a chicken, cut along each side of the backbone with shears. Remove the backbone, and reserve it for stock (it can be frozen up to three months). Turn the bird breast side up; flatten it with your palm.
If your grill is big enough, double the recipe. Leftovers are delicious cold over salad.