We have searched in p p̄ collisions at √s = 1.8 TeV for events with three charged leptons and missing transverse energy. In the minimal supersymmetric standard model, we expect trilepton events from chargino-neutralino (χ̃1±χ̃20) pair production, with subsequent decay into leptons. We observe no candidate e+e-e±, e+e-μ±, e+μl+μ-, or μ+μ μ± events in 106 pb-1 integrated luminosity. We present limits on the sum of the branching ratios times cross section for the four channels: σχ̃1±χ̃2 0B(χχ̃1± χ̃20 → 3ℓ + X) < 0.34 pb, Mχ̃1± > 81.5 GeV/c2, and Mχ̃20 > 82.2 GeV/c2 for tan β= 2, μ = -600 Gev/C2, and Mq̃ = Mg̃.
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