The NuTeV Collaboration has observed an excess in their di-muon channel, possibly corresponding to a long-lived neutral particle with only weak interactions and which decays to muon pairs. We show that this can not be explained by pair production of neutralinos in the target followed by their decay far downstream in the detector via a LLE R-parity violating (RPV) operator, as suggested in the literature. In the parameter region allowed by LEP the event rate is far too small. We propose instead a new neutralino production method via B-mesons, which can fully explain the observation. This is analogous to neutrino production via -mesons. This model can be completely tested and thus also possibly excluded with NOMAD data. If it is excluded, the NuTeV observation is most likely not due to physics beyond the Standard Model. Our model can also be tested at the current and future B-factories. This opens up a new way of testing a long-lived neutralino LSP at fixed-target experiments and thus a possibility to close the gap between collider and cosmological tests of R-parity violation. We also discuss a possible explanation in terms of a neutral heavy lepton mixing with the Standard Model neutrinos. The flavour structure of the observation can be accounted for but the production rate is far too low.