We propose a new explanation for the dilepton excess observed in dense (hot) nuclear matter at invariant masses below 1GeV.We argue that the presence of local parity breaking due to a time-dependent isosinglet and/or isotriplet pseudoscalar condensate may substantially modify the dispersion relation of photons and vector mesons propagating in such a medium, resulting in an abnormally large excess of e+e−pairs with respect to the common theoretical predictions based on a “cocktail” of hadronic processes. We propose various signatures to prove or disprove this effect.