1) Preheat the oven to 190C/Gas Mark 5.
2) Season the chicken cavity with salt and pepper. Tie the legs together with kitchen string and fold the wing tips under the back. Put the carrot, onion, celery, neck, and heart, if using, in the center of a roasting tin just large enough to accommodate the chicken. (Discard the liver or reserve for another recipe.)
3) Season butter with salt and pepper and brush the entire chicken with it. Set the bird breast-side up on top of the vegetables.
4) Roast the chicken for 45 minutes. Then increase the temperature to 220C/Gas Mark 8, cooking until an instant-read thermometer stuck into the chicken thigh registers 71 to 76C, about 15 minutes more. Tip the chicken so the juices run into the tin.
5) Transfer the chicken to a cutting board and loosely tent with foil while making the jus.
For the jus:
1) Set a strainer over a bowl. Strain the vegetables, giblets, if using, and pan juices into the strainer. Shake the strainer to get more juices into the bowl. Set strainer aside.
2) Skim most of the fat from the surface of the liquid with a spoon, or alternately, use a degreasing cup. Reserve the pan juices.
3) Place the roasting tin directly on a burner set at medium-high. Pour the chicken stock into the tin, and scrape the tin with a wooden spoon to loosen all the browned bits that cling to the tin.
4) Add the reserved pan juices, increase the heat to high and boil the liquid until slightly thickened. Return the reserved vegetables to the sauce, if desired, or carefully strain jus through a fine sieve into a serving bowl.
5) Taste and season with salt and pepper. Keep warm until ready to serve.
6) Carve the chicken and serve with the jus.
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