To prepare the meat, tip all the ingredients, except for the chicken and ketchup, into a blender or mini processor. Add a pinch of salt and blitz to a rough paste. Tip two-thirds of the paste into a large bowl with the chicken, and massage the marinade into the meat. Cover and leave for at least 1 hr at room temperature, or up to 48 hrs in the fridge.
Meanwhile, make the barbecue sauce. Tip the remaining paste into a small saucepan and bring to a simmer. Cook for 5 mins until it thickens and becomes darker, then add the ketchup and cook for 5 mins until sticky. Tip into a container and set aside.
Light the barbecue, ensuring the coals are piled up at one end and leaving only a couple of coals on the other side. Lay the chicken on the emptier side. If you’re making the smoke mix, carefully scatter all of the ingredients directly onto the piled-up coals. Cover the barbecue (with the vents open) and cook the chicken for 20 mins. Remove the lid and turn the chicken, then cover again and cook for a further 20 mins.
Remove the lid and move the chicken across the grill so it’s above the piled-up coals, then baste with some of the barbecue sauce, keeping enough aside, in a separate container, to serve later. Cook for 10 mins, adding a few more coals if you need to and turning often, until nicely charred and cooked through – a digital thermometer inserted through the thickest part of the meat should read at least 65C.
Put the lime halves on the grill, over the coals, cut-side down for 3-4 mins until charred. Serve the chicken with the lime for squeezing over and reserved barbecue sauce for dipping.