We have searched for chargino-neutralino production (chi-bar^+/-_1
chi-bar^0_2) in 1.8 TeV pp-bar collisions, followed by their leptonic decays
chi-bar^+/-_1 -> chi-bar^0_1 1^+/- nu and chi-bar^0_2 -> chi-bar^0_1 l^+ l^-.
These trilepton events are expected within a framework of the Minimal
Supersymmetric Standard Model (MSSM).  In a 19.1 pb^-1 data sample collected
with the Collider Detector at Fermilab, no trilepton events were observed.
Upper limits on sigma(pp-bar -> chi-bar^+/-_1 chi-bar^0_2) . BR(chi-bar^+/-_1
chi-bar^0_2 -> 3l + X) were obtained for various MSSM parameter space
regions, yielding new 95% confidence level lower limits for the neutralino
(chi-bar^0_2) mass which extended as high as 49 GeV/c^2.