Preheat the oven to 180 C or 350 F.
Clean the chicken thighs and legs and pat them dry on a paper towel
In a ziplock bag, combine the paprika, oilve oil and salt.
Add the chicken pieces to the bag, seal the bag, and and coat them well in the marinade by tossing the pieces in the bag.
Zest the clementines or orange, and keep the zest aside. Then slice the oranges finely and keep the slices aside.
In a bowl, combine the orange zest, chopped olives, minced garlic.
Get the marinated chicken pieces out of the bag, and with your fingers, gently create a space between the chicken skin and the meat.
Stuff the zest-garlic-olive mixture under the skin and keep aside.
In a baking tray or roasting pan lined with foil, scatter the sliced carrots and the orange slices.
Place a grilling rack right over the baking tray, and place the chicken pieces on the grill, so that the juices from the chicken drip down on the carrots and orange slices as they cook.
Transfer the grill rack and the tray into the oven and grill for around 50 minutes in the oven, until the chicken skin crisps up well.
At the halfway mark, flip the chicken over so that it cooks evenly.