Preheat the oven to 200°C/180°C fan/gas 6.
Rub the chicken with the oil and lemon juice, salt and pepper and push the squeezed half lemon inside the cavity. Lay the chicken, breast-side down, in a baking dish and pour in about 5 tablespoons water. Roast for 1 hour then turn the chicken breast-side up and roast for another 15–20 minutes, until the skin is crisp and brown and the juices run clear when you cut into the bird between the leg and the body with a pointed knife.
While the chicken is in the oven, make the bulgur pilaf: in a large frying pan, fry the onion in the oil over medium heat, with the lid on, for about 20 minutes until brown and caramelised. Stir often and remove the lid towards the end.
At the same time, bring the chicken stock to the boil in a large pan. Stir in the cinnamon, allspice, coriander and some salt (taking into consideration the saltiness of the stock). Stir in the raisins and bulgur and cook over low heat, with the lid on, for about 10 minutes or until the liquid has been absorbed and the grain is tender. Fold in the butter, and add pepper, and more salt to taste.
Put the pine nuts and chestnuts in the frying pan with the fried onions and cook, stirring, for 2–3 minutes, then mix into the bulgur.
For the yoghurt sauce, beat the yoghurt with the rest of the ingredients with a fork.
To serve, cut the chicken into pieces and pour the lemony sauce that has formed at the bottom of the baking dish over the chicken and the bulgur. Serve with the yoghurt sauce.