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.

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