The growth of rubrene (C42H28, 5,6,11,12-tetraphenylnaphthacene) multilayer islands up to a thickness of six layers on a Au(111) surface has been investigated by scanning tunneling microscopy. The molecules self-organize in parallel twin rows, forming mirror domains of defined local structural chirality. Each layer is composed of twin-row domains of the same structural handedness rotated by 120 degrees with respect to each other. Moreover, this structural chirality is transferred to all successive layers in the island, resulting in the formation of three-dimensional objects having a defined structural chirality. The centered rectangular surface unit cell differs from the one characteristic for the single-crystal orthorhombic phase.