Preheat oven to 425°F with rack in upper third position. Whisk ⅓ cup oil, ⅓ cup lemon juice, 1½ tablespoons za’atar, ¾ teaspoon salt and ½ teaspoon pepper together in a large bowl until combined. Add chicken, rinsed chickpeas and onion wedges; toss until coated. Spread in an even layer on a large rimmed baking sheet, placing the chicken skin-side up. Arrange lemon slices and garlic halves, cut-sides down, around the chicken.
Roast until the chicken is browned and an instant-read thermometer inserted into the thickest portion registers 165°F, about 35 minutes. Squeeze garlic cloves from their skins onto the chickpea mixture; discard the skins. Sprinkle the mixture with ½ cup feta and ¼ cup cilantro leaves.
