We have searched in pp ̄ collisions at √s=1.8TeV for events with three charged leptons and missing transverse energy. In the minimal supersymmetric standard model, we expect trilepton events from chargino-neutralino (χ̃±1χ̃02) pair production, with subsequent decay into leptons. We observe no candidate e+e−e±, e+e−μ±, e±μ+μ−, or μ+μ−μ± events in 106pb−1 integrated luminosity. We present limits on the sum of the branching ratios times cross section for the four channels: σχ̃±1χ̃02B(χ̃±1χ̃02→3l+X)<0.34pb, Mχ̃±1>81.5GeV/c2, and Mχ̃02>82.2GeV/c2 for tanβ=2, μ=−600GeV/c2, and Mq̃=Mg̃.
