Rinse the chicken pieces under cold water and pat dry with paper towels. Place in a baking dish large enough to hold the pieces in a single layer.
In a small bowl, combine the vinaigrette with the lemon zest, olives, garlic, thyme, and 1/2 teaspoon of the salt. Pour the mixture over the chicken and turn to coat. Refrigerate, covered, for at least 1 hour or overnight.
Heat oven to 425° F. Season the chicken with the pepper and the remaining 1/2 teaspoon of salt. Roast until golden brown, about 20 minutes. Reduce heat to 375° F. Continue to roast until the chicken is cooked through, about 40 minutes more.
Spoon the olives and pan juices over the chicken and serve.