Combine mustard, chopped shallot and cayenne pepper in a bowl.
Put the olive oil or butter in a roasting pan and put it in the oven for a couple of minutes until the oil is hot or the butter melts.
Roll the chicken in the mustard mixture until coated thoroughly.
Remove the pan from the oven, add the chicken and return to oven. Roast the chicken, turning once or twice, for 10 to 15 minutes or until cooked through. All traces of pink should vanish - internal tem of 155 degrees. Use any extra mustard mixture to baste the breasts as they cook.