Single production of SUSY particles in the decays of the Z0 may proceed with large rates in models with spontaneously broken R-parity. We focus on the case where there is a lepton number symmetry as part of the gauge group. In the simplest of such models there is a single additional neutral gauge boson and the strength of Rp-violating interactions is related with that of the new gauge force. We study the phenomenological implications of the model for Z0 decays, including the study of the rates for single chargino production in Z0 decays, i.e. Z0→ξ±τ±, as well as for the so-called Zen events, and find that they may be measurable at LEP. The first process, characteristics of spontaneously broken R-parity models, may proceed with a branching ratio as large as few × 10−5 and should lead to a very clear signature. Zen events have a different origin than in the minimal SUSY standard model (MSSM). Their rates may also be enhanced with respect to MSSM. Our estimates of these rates take into account all of the relevant observational constraints, such as those that follow from neutrinophyics, from precise Z0 property measurements, as well as SUSY particle searches at LEP.