Put the chicken in a large nonmetalic bowl. Put the orange and lime zests in a small bowl and add the fruit juices. Whisk in the olive oil, garlic, 1 teaspoon salt, and a generous grind of black pepper. Pour the marinade over the chicken and toss until well coated. Marinate for 20 to 30 minutes but no longer than 45 minutes.
Preheat the oven to 375 degrees F. Put a rack on a rimmed baking sheet. With tongs, remove the chicken pieces from the marinade and arrange them on the rack leaving space between each piece. Drizzle a small spoonful of the marinade over the top of each chicken piece; season well with salt and pepper, to taste. Roast until the chicken is cooked through and the juices run clear when meat is pierced with a knife, about 45 minutes.
Transfer the chicken to a serving platter. Cool slightly before serving or let stand until room temperature before refrigerating for later use.