For the salad:
For the dressing:
Preheat the oven to 425˚ F. Adjust oven racks to upper- and lower-middle positions. Line a baking sheet with foil. On the baking sheet, combine the squash with 2 tablespoons of the oil. Season generously with salt and pepper and toss to combine. Place the baking sheet on the lower oven rack and roast until fork tender, about 20-25 minutes, tossing once during cooking.
Meanwhile, place the chicken on a second rimmed baking sheet lined with foil. Drizzle lightly with the remaining olive oil. Season with salt and pepper. Place on the upper oven rack and roast until cooked through (160˚ F internal temperature on an instant read thermometer), about 15-20 minutes. Set aside to rest briefly, then slice.
To make the dressing, in a small bowl, combine the tahini, olive oil, lemon juice, oregano and garlic. Whisk together to blend. Whisk in the water, adding more as needed until the dressing has reached your desired consistency. Season to taste with salt and pepper.
Divide the lettuce up between serving plates. Top each serving with some of the squash, chicken, chickpeas, pita and chips. Drizzle lightly with the tahini dressing. Sprinkle with the minced chives. Serve immediately.