Using the upper bound on the effective number of light neutrino species during primordial nucleosynthesis and the cosmological pion-pole mechanism [gamma][gamma][r arrow][pi][sup 0][r arrow][gamma][ital X], we obtain an upper limit on the branching ratio for the decay [ital B]([pi][sup 0][r arrow][gamma][ital X])[lt]3[times]10[sup [minus]13], where [ital X] is any long-lived weakly interacting neutral vector particle with a mass smaller than the neutral pion mass.