  We present results of the first search for like-sign dilepton (ee, e\mu,
\mu\mu) events associated with multijets and large missing energy using 106
pb^-1 of data in p-pbar collisions at sqrt(s)=1.8 TeV collected during 1992-95
by the CDF experiment. Finding no events that pass our selection, we examine
pair-production of gluinos and squarks in a constrained framework of the
Minimal Supersymmetric Standard Model. At tan_beta = 2 and \mu=-800 GeV/c^2, we
set 95% confidence level limits of M(gluino) > 221 GeV/c^2 for M(gluino) \simeq
M(squark), and M(gluino) > 168 GeV/c^2 for M(squark) \gg M(gluino), both with
small variation as a function of \mu.
