In a large bowl, whisk together oil, lemon zest, garlic, zaatar, lemon juice, salt, and pepper. Add chicken and turn to coat. Transfer chicken and marinade to a resealable plastic bag and seal. Chill in a refrigerator or cooler.
Build a wood fire in a fire ring (see "Learn to Cook over Live Fire," below) and let it burn down to medium heat (about 350°; you can hold your hand 5 inches above cooking grate only 5 to 7 seconds).
Grill chicken, turning every 5 to 8 minutes, until well browned and cooked through, 20 to 30 minutes total; watch for flare-ups and move chicken to a cooler spot if needed. During last few minutes, grill lemon wedges and onions, turning once, just until grill marks appear. Serve with chicken.
*Find in the spice aisle of well-stocked grocery stores and at worldspice.com.
Make ahead: Through step 1, up to 1 day, chilled, or up to 2 weeks, frozen; thaw in cooler.
Wine pairing: An earthy, lighter-bodied red like La Follette Pinot Noir (North Coast), with mushroom and forest floor notes combined with violets and peppery cherry fruit that make a perfect foil for the za'atar on the chicken.
Learn to Cook over Live Fire:
When you're cooking anything more advanced than s'mores, you need a campfire that will work with you. Our favorite design is a log cabin-style arrangement surrounding a tipi of kindling. In a fire ring, stack four large logs in a box shape (use six if you're planning a long cooking time). Add tinder inside the box and arrange kindling in a tipi over it. Light tinder with matches or a lighter in a couple of spots; when it starts smoking, blow gently until flames emerge. It takes 1 to 1 1/2 hours for a campfire to burn down to low flames and embers, the ideal stage for cooking. At that point, spread the fire evenly under the cooking grate, using grilling tongs. Move logs or add more of them as needed.
Camp Sunset, a Modern Camper's Guide to the Great Outdoors (Oxmoor House; May 2016)