Sheet-Pan Chicken with Zucchini and Garlicky Tomato Relish

Preheat oven to 450°F. Rub chicken all over with 2 tablespoons of the oil. Season all over with 1 teaspoon of the salt and 1/4 teaspoon of the pepper. Place on a rimmed baking sheet. Toss together shallots, zucchini, 1/2 teaspoon of the salt, and remaining 1/4 teaspoon pepper in a medium bowl. Scatter zucchini mixture around chicken. Bake 25 minutes, rotating baking sheet halfway through bake time. Increase oven temperature to broil. (Do not remove baking sheet from oven.) Broil until chicken is cooked through and skin is lightly browned, 2 to 4 minutes. While chicken roasts, stir together tomatoes, vinegar, tarragon, garlic, and remaining 6 tablespoons oil and 1 teaspoon salt. Transfer chicken and zucchini mixture to a platter. Immediately add tomato mixture to hot baking sheet, and place over medium. Using a flat wooden spoon or spatula, scrape up browned bits from bottom of baking sheet while tomatoes release their juices. Immediately pour tomato salsa over chicken and vegetables, and serve.