We report an unusually strong flow-induced birefringence in an optically isotropic cubic phase occurring below the isotropic chiral conglomerate phase formed by a low-molecular-weight polycatenar mesogen. The transition into the birefringent state occurs thresholdless and the induced birefringence is comparable with that observed in polymeric systems. We suggest that the flow-induced deformation of the cubic structure is responsible for the strong rheo-optical response.