Self-assembly of conjugated 2,5-dialkoxy-phenylene-thienylene-based oligomers on epitaxial monolayer graphene was studied in ultrahigh vacuum by low-temperature scanning tunneling microscopy (STM). The formation of long one-dimensional (1D) supramolecular chain-like structures has been observed, associated to a physical linking of their ends which involved the rotation of the end thiophene rings in order to allow pi-pi stacking of these end-groups. dI/dV maps taken at an energy corresponding to the excited states showed a continuous electronic density of states, which tentatively suggests that within such molecular chains conjugation of electrons is preserved even across physically linked molecules. Thus, in a self-organization process conjugation may be extended by appropriately adapting conformations of neighboring molecules. Our STM results on such self-organized end-linked molecules potentially represent a direct visualization of J-aggregates.