1. Heat oven to 400 degrees F. Pat the chicken dry inside and out with paper towels. Remove giblet package, if present. Being careful not to tear it, use your fingers to gently separate the skin from the breast meat and slide 2 or 3 slices of citrus under the skin on each side. Place remaining citrus slices in the chicken cavity, squeezing to release some of the citrus juice. Rub olive oil all over the chicken and sprinkle with kosher salt and pepper. Place chicken in a roasting pan or heatproof baking dish.
2. Roast, uncovered, for 25 minutes. Add carrots or parsnips to the pan or dish; sprinkle lightly with salt and toss to coat. If chicken is browning to fast, cover loosely with foil. Roast another 35 to 45 minutes or until an instant-read thermometer registers 170 degrees F. in the breast or 180 degrees F. in the thigh and carrots or parsnips are tender, stirring vegetables once more during cooking.
3. Remove chicken from oven and let stand 10 minutes.