Preheat the oven to 400 degrees F. Line a baking tray with foil.
Place the softened butter in a bowl with the lemon zest. Strip the leaves from 1 sprig of rosemary, finely chop and add along with some salt and pepper. Mix everything together.
Lay the chicken on the foil-lined baking tray, breast-side up. Use your fingers to smear the butter mixture all over the chicken, under the skin and inside the cavity.
Squeeze the juice of 1 of the lemons over the chicken, and then place the 4 lemon halves (if they fit!) inside the cavity of the chicken along with the 3 whole remaining sprigs of rosemary.
Put the chicken in the oven and roast it until done, about 1 hour 15 minutes. The skin should be deep golden brown and the juices should be sizzling.