We performed an ultra-high vacuum scanning tunneling microscopy (STM) investigation of the self-assembly of rubrene at room temperature on Cu(111), a metal surface with threefold symmetry. Rubrene self-assembles into two different structures called row and trimer. Both are different than the structures already observed on Cu(110) and Cu(100). Row and trimer structures have comparable molecular packing densities and are equally distributed across the surface. In the row structure the molecules are oriented with their backbone along the same high symmetry directions of the surface: [[Formula: see text]], [[Formula: see text]] or [[Formula: see text]]. The trimer structure is composed of units of three rubrene molecules, oriented along the high symmetry surface directions. These units are chiral, as revealed by height profile measurements by STM, and self-assemble in domains containing only one type of enantiomer.