Place the butter on a plate and set it aside to soften.
Heat oven to 425 F and begin preparing the vegetables. Scrub the potatoes. Peel the carrots, halve them lengthwise, and cut them crosswise into 2-inch pieces.
Place the vegetables in a large roasting pan or baking dish and toss with the olive oil, teaspoon salt, and teaspoon pepper.
Remove the neck and the bag of giblets from inside the cavity of the chicken and discard them. Pat the chicken dry with paper towels. Prick the lemon several times with a sharp paring knife and place it in the chicken cavity with the thyme. Rub the outside of the chicken with the softened butter and season with teaspoon salt and teaspoon pepper. Tie the legs together with kitchen twine. Place on top of the vegetables in the roasting pan.
Put the chicken in the oven and roast until the vegetables are tender, the chicken is golden brown, and the juices run clear when the thigh is pierced with a fork, 65 to 75 minutes. (If you use an instant-read thermometer, it should register 165 F when inserted in the thickest part of the thigh.) Let the chicken rest for at least 10 minutes before carving.
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