Rub the chicken with salt and pepper. In a small bowl, combine the butter and chopped dill. Rub the chicken with about 2 tablespoons of the dill butter. Carefully lift up the skin from the chicken breasts at the cavity, using your fingers or a blunt knife to loosen the skin; be careful not to tear it. Insert about 1 tablespoon of the dill butter under the skin of the breast and make sure that the skin covers the meat when you are done. Refrigerate the remaining butter. Fill the cavity of the chicken with the lemon quarters and the bunch of dill.
Place the chicken breast side up on a V-shaped rack in a roasting pan. Place the roasting pan on the middle oven rack and roast the chicken for 25 minutes.
Remove the chicken from the oven and rub with about 1 tablespoon of the dill butter, holding the butter in your fingers. When most of the butter has melted and you are at risk of burning your fingers, place the remaining lump on the breast of the chicken.
Remove the roasting pan from the oven. Fill the pan with the leeks, potatoes, and garlic and add the chicken stock. Turn the chicken breast side down and place it in the roasting pan. Reduce the oven temperature to 350°F. Return the roasting pan to the oven and roast for 50 to 60 more minutes, or until the chicken is cooked through. Test for doneness by piercing it with a sharp knife at the thickest part of the thigh; the juices should run clear. (If there is any trace of pink in the juices, return the chicken to the oven.) Transfer the chicken to a carving board and let it rest, uncovered, for 15 minutes.
Check the potatoes for doneness. If they are still firm, increase the oven temperature to 400°F and continue baking until the potatoes are nice and tender. Squeeze the garlic out of their skins. Leave the roasting pan in the oven with the heat turned off.
Transfer the potatoes, leeks, and garlic to a serving platter. Carve the chicken at the table (discard the lemon and dill inside the cavity).
Garnish with dill and lemon wedges and sprinkle lemon zest on top.