By design, coupled mechanical oscillators offer a playground for the study of crystalline topology and related properties. Particularly, non-centrosymmetric, supramolecular nanocrystals feature a complex phonon spectrum where edge modes may evolve. Here we show, employing classical atomistic calculations, that the edges of a chiral supramolecular nanoribbon can host defined edge phonon states. We suggest that the topology of several edge modes in the phonon spectrum is nontrivial and thermally insulated from bulk states. By means of molecular dynamics, we excite a supramolecular bond to launch a directional excitation along the edge without considerable bulk or back-propagation. Our results suggest that supramolecular monolayers can be employed to engineer phonon states that are robust against backscattering, toward supramolecular thermal waveguides, diodes, and logics.