  We report a search for the anomalous production of events with multiple
charged leptons in p-pbar collisions at sqrt{s} = 1.96 TeV using a data sample
corresponding to an integrated luminosity of 346 pb^{-1} collected by the CDF
II detector at the Fermilab Tevatron. The search is divided into three-lepton
and four-or-more-lepton data samples. We observe six events in the three-lepton
sample and zero events in the >=4-lepton sample. Both numbers of events are
consistent with standard model background expectations. Within the framework of
an R-parity violating supergravity model, the results are interpreted as mass
limits on the lightest neutralino and chargino particles. For one particular
choice of model parameters, the limits are M_neutralino > 110 GeV/c^{2} and
M_chargino > 203 GeV/c^{2} at 95% confidence level; the variation of these mass
limits with model parameters is presented.
