Search for Chargino-Neutralino Associated Production at the Fermilab Tevatron Collider

We have searched in $p \bar{p}$ 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 ($\chione \chitwo$) pair production, with subsequent decay into leptons. We observe no candidate $e^+e^-e^\pm$, $e^+e^-\mu^\pm$, $e^\pm\mu^+\mu^-$ or $\mu^+\mu^-\mu^\pm$ 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_{\chione\chitwo}\cdot $BR$(\chione\chitwo\to 3\ell+X) < 0.34$~pb, M$_\chione > $ 81.5 \mgev\sp and M$_\chitwo > $ 82.2 \mgev\sp for $\tan\beta=2$, $\mu =-600$~\mgev\sp and M$_\squark=$ M$_\gluino$.