Peel the grapefruit so that the white skin is completely removed. Remove the fillets with a sharp knife between the parting skins. Roast sesame seeds in a pan without fat. Wash the chives, shake dry and cut the stalks into small rolls.
Stir cream cheese until smooth. Stir in chives and season to taste with salt and pepper.
Cut the ham slices in half crosswise. Spread with cream cheese and place 1 grapefruit fillet diagonally on each. Whip the ham over the grapefruit and cut in half again. Stick together with the skewers.
Sprinkle packets of ham with sesame seeds.