A theoretical analysis of emission in oligo-p-phenylene vinylene herringbone aggregates shows that the radiative decay rate of the lower exciton band-edge can exceed that of a single molecule. Such superradiant H-aggregates require long-range orientational order and constructive interference between the off-axis molecular transition dipole moments. Excellent agreement with the experimental emission spectrum of p-distyrylbenzene nanoaggregates is obtained. Extensions are made to superradiant polymer aggregates, which could have important optical device applications.