From the interplay of scanning tunneling microscopy and theoretical calculations, we study the chiral self-assembly of achiral HtB-HBC molecules upon adsorption on the Cu(110) surface. We find that chirality is expressed at two different levels: a +/- 5 degrees rotation of the molecular axis with respect to the close-packed direction of the Cu(110) substrate and a chiral close-packed arrangement expected for star-shaped molecules in 2D. Out of the four possible chiral expressions, only two are found to exist due the effect of van der Waals (vdW) interactions forcing the molecules to simultaneously adjust to the atomic template of the substrate geometry and self-assemble in a close-packed geometry.