We have searched in ppbar collisions at sqrt 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 (chi\bar~^+\- _1 chi\bar~^0_2) pair production, with
subsequent decay into leptons.  We observe no candidate e^+ e^- e^+\-,
e^+ e^- mu^+\-, e^+\- mu^+ mu^- or mu^+ mu^- mu^+\- events in 106 pb^-1
integrated luminosity.  We present limits on the sum of the branching ratios
times cross section for the four channels: sigma_chi\bar~^+\-_1 chi\bar~^0_2
-> 3l + X) < 0.34 pb, M_chi\bar~^+\-_1 > 81.5 GeV/c^2 and M_chi\bar~^0_2 >
82.2 GeV/c^2 for tan beta = 2, mu = -600 GeV/c^2 and M_q\bar~ = M_g\bar~.