How to Make It
Heat oven to 425° F, with the racks in the upper and lower thirds. On a rimmed baking sheet, toss the squash with 2 tablespoons of the oil, ½ teaspoon salt, and ¼ teaspoon pepper. Roast on the bottom rack, tossing once, until tender, 25 to 30 minutes.
Meanwhile, place the chicken on a second rimmed baking sheet and coat it with 1 tablespoon of the remaining oil; season with ¼ teaspoon each salt and pepper. Roast on the top rack until cooked through, 15 to 20 minutes. Let cool slightly, then slice.
Meanwhile, in a small bowl, whisk together the tahini, lemon juice, oregano, the remaining tablespoon of oil, ⅓ cup water, and ¼ teaspoon each salt and pepper. Divide the lettuce among plates; dividing evenly, top with the squash, chicken, chickpeas, pita chips, and chives. Serve with the dressing.