We demonstrate that exciton conductance in organic materials can be enhanced by several orders of magnitude when the molecules are strongly coupled to an electromagnetic mode. Using a 1D model system, we show how the formation of a collective polaritonic mode allows excitons to bypass the disordered array of molecules and jump directly from one end of the structure to the other. This finding could have important implications in the fields of exciton transistors, heat transport, photosynthesis, and biological systems in which exciton transport plays a key role.