Put the ham slices in a non-aluminum pan just large enough to hold them side by side.
Mix the rum, clove, garlic, thyme, orange rind, and sugar and rub over both sides of each slice. Let marinate for 1 hour. Pour over the chicken stock and simmer covered very slowly until the ham is tender, about 1½ hours.
While the ham is cooking, peel the oranges, cut out the sections b