If your chicken is frozen, be sure to thaw it 1-2 days in advance. When ready to prepare, preheat oven to 450 degrees F and adjust your oven rack so the chicken will sit in the center of the oven.
Remove neck and giblets from inside the cavity of the chicken and pat dry all over with paper towels.
In a bowl, combine softened butter, zest of the lemon, and chopped rosemary. Season the outside of the chicken and inside the cavity with salt and pepper. Cut the lemon in half and place inside the cavity of the bird.
Use your fingers to loosen and lift the skin above the breasts (on the top of the chicken) and smooth a few tablespoons of the herb butter underneath.
Microwave the remaining herb butter mixture for 10 seconds (it doesn’t need to be melted, just softened). Smear the remaining herb butter all over the outside of the chicken, legs and wings.
Add the onion, carrot and potato to the bottom of a 9x13 inch baking dish. Drizzle a little olive oil over the veggies, season them with salt and pepper, and toss to coat. Place the chicken on top, and tie the legs together with kitchen twine if you want (not required).
Roast the chicken, uncovered, at 450 degrees F for 10-15 minutes. Then reduce the temperature to 350 degrees F and roast for 20 minutes per pound, or until internal temperature (inserted on middle of thigh and breast) reaches about 165 degrees. Skin should be golden brown and the juices should run clear.
*Check the chicken about halfway through cooking and if the skin is getting overly brown you can cover it with a piece of tinfoil to protect the breast meat from overcooking.
Remove chicken from the oven and cover with tinfoil. Allow it to rest for 10 minutes before carving. Serve with the cooked vegetables at the bottom of the pan.
Optional: reserve the drippings in the roasting pan to make chicken gravy.