Stir together yogurt, 1 tablespoon chives, and 1/8 teaspoon salt. Season with pepper.
Cut away peel and pith from grapefruit, keeping segments intact. Cut between membranes using a sharp paring knife to release segments. Slice each grapefruit segment into 3 long, thin slices. (Alternatively, cut grapefruit into small chunks.)
Arrange cucumber slices on a platter and dollop yogurt mixture onto the center of each (about 1/2 teaspoon per slice). Top each with 1 gravlax square and 1 grapefruit slice (twisting together if desired; you may have extra grapefruit slices). Sprinkle with remaining tablespoon chives.