  We have searched for chargino-neutralino production (\chichi) in 1.8 TeV
\ppb\sp collisions, followed by their leptonic decays
\chione\dk\chizero\lnu\psp and \chitwo\dk\chizero\lplm. 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
$\sigma(\ppb\dk\chichi)\cdot BR(\chichi\dk 3 \ell + X)$ were obtained for
various MSSM parameter space regions, yielding new 95\% confidence level lower
limits for the neutralino (\chitwo) mass which extended as high as 49 \mgev.
