A closed expression for the Stark signal of molecular aggregates, which does not suffer from singularities when the exciton states are nearly degenerate and avoids the calculation of two-exciton states, is derived from the third order response to the total (static + optical) field, treating intermolecular interactions within the local field approximation. Transitions between one-exciton states play an important role and generally reduce the magnitude of the signal with respect to monomer spectra. The experimental Stark spectrum from the B820 dimer subunit of LH1 is consistent with simulations for a dimer of parallel pigments. The spectra of LH1 and LH2 cannot be explained by excitonic interactions alone. This supports the idea that charge-transfer states may play an important role in the spectroscopy of photosynthetic pigment proteins.