Score the duck breasts and season with salt and pepper.
Heat the olive oil in a frying pan until hot then add the duck, skin side down. Cook for 5-8 mns then turn and cook for 5 mns on the other side for pink, longer for medium. Remove from the pan and set aside.
Drain off the excess fat from the pan. And return to the heat. Add the vinegar, oil and honey, scraping the bottom of the pan to blend the residue into the sauce. Add half the orange juice, the orange segments and the orange and lime zests then whisk in half the butter.
In a separate pan heat the remaining butter with a splash of oil and sauté the chicory leaves until softened. Season and add the caster sugar to caramelise the leaves.
Slice the duck breasts and serve with the chicory and sauce.