For the chicken, in a large pan on a high heat cook the red wine and port until the volume of liquid has reduced by three-quarters. Remove from the heat and add the garlic, bay, thyme and lemon zest. Season to taste and set aside to cool.
Add the cooled marinade to the chicken and work it in well, ensuring that you lift the skin away from the breasts and get the marinade under the skin. Cover with cling film and refrigerate overnight to marinade.
Remove the chicken from the fridge, discard the cling film and allow the chicken to sit at room temperature for an hour.
Preheat the oven to 150C/300F/Gas 2.
Place the chicken and its marinade in a roasting tray. Cover with foil and pierce the foil a few times with a knife. Place in the oven for an hour. By pre-cooking the chicken at a low temperature you ensure that you get juicy meat. Remove the chicken from the oven and reserve any juices in the roasting tray.
Meanwhile for the remoulade, in a medium bowl, whisk together the egg yolk and mustard until a pale colour. Continuing to whisk, slowly add the oil, drop by drop until the egg begins to thicken and the dressing turns to mayonnaise. Add the oil in a thin steady stream until it is all incorporated.
Whisk in the vinegar, salt, pepper and lemon juice. Taste and correct the seasoning and then mix in the celeriac. Set aside in the fridge.
Preheat your barbecue to about 150C/300F and lightly oil the grill bars with sunflower oil.
Lay the chicken, skin-side down in the centre of the barbecue and cook for seven minutes with the lid closed. Turn the chicken over and cook for another five minutes with the lid closed. Baste with the reserved cooking liquid.
Remove from the barbecue to a carving board and allow to rest for 10 minutes. Joint the chicken and carve the breasts into long strips.
Serve with the remoulade alongside.