  The control of exciton transport in organic materials is of fundamental
importance for the development of efficient light-harvesting systems. This
transport is easily deteriorated by traps in the disordered energy landscape.
Here, we propose and analyze a system that supports topological Frenkel exciton
edge states. Backscattering of these chiral Frenkel excitons is prohibited by
symmetry, ensuring that the transport properties of such a system are robust
against disorder. To implement our idea, we propose a two-dimensional periodic
array of tilted porphyrins interacting with a homogenous magnetic field. This
field serves to break time-reversal symmetry and results in lattice fluxes that
that mimic the Aharonov-Bohm phase acquired by electrons. Our proposal is the
first blueprint for realizing topological phases of matter in molecular
aggregates and suggests a paradigm for engineering novel excitonic materials.
