Heat oven to 425 degrees. On a rimmed baking sheet, combine squash and chickpeas with 3 tablespoons oil; season well with salt and pepper. Toss to coat, then spread in an even layer. Rub chicken with 1 tablespoon oil, season with salt and pepper, and arrange on top, skin-side up. Roast for 20 minutes, then stir in dates, and roast until squash is golden and chicken is cooked through, about 20 to 25 minutes longer.
Step 2
While the mixture roasts, in a small bowl, whisk the remaining 1/4 cup oil with the olives, parsley, capers and caper brine, and lemon juice. Season the olive relish with salt and pepper, then set aside.
Step 3
Divide the roasted chicken, squash, dates and chickpeas among plates. Stir any pan juices into the relish, then spoon the relish on top of each serving. Serve with lemon wedges.