Place the chicken pieces in a buttered shallow roasting tin or baking dish. Choose one big enough to take both chicken and vegetables. Season the chicken with the salt and freshly milled pepper. Cream the butter until soft, then beat in the chopped parsley and lemon juice. Spread the parsley butter generously over the chicken joints. Place in the centre of a moderate oven (180 °C., 350 °F., Gas Mark 4) and bake for 1 hour.
Meanwhile trim either end of the courgettes, wash and slice thickly. Add to a pan of boiling salted water, bring back to the boil and simmer for 2–3 minutes to blanch the slices, then drain well. (If new potatoes are used, make sure to select small potatoes which will cook quickly, and blanch as for the courgettes.) Add the courgettes to the chicken after about 15 minutes of the baking time. Turn the courgettes in the parsley butter which will have begun to melt around the sides of the baking dish. Baste the chicken joints and replace in the oven to complete cooking time. Baste chicken and courgettes occasionally.
Serve the chicken with the vegetables, butter and juices from the pan.