Whisk together oil, zaatar, lemon juice, zest, garlic, salt, and pepper in a large bowl. Add chicken and turn to coat.
Heat grill to medium (350° to 450°). Grill chicken, skin side down, until browned, 5 to 8 minutes; watch for flare-ups and move chicken to a cooler spot if needed. Turn chicken and grill until cooked through, about 4 minutes.
Grill lemon wedges and onions in last few minutes, turning once, just until grill marks appear. Serve with chicken.
*Find the Middle Eastern spice blend in the spice aisle of well-stocked grocery stores and at worldspice.com