We present results of the first search for like-sign dilepton ( e(+/-)e(+/-), e(+/-)mu(+/-), mu(+/-)mu(+/-)) events associated with multijets and large missing energy using 106 pb(-1) of data in pp macro collisions at square root of s = 1.8 TeV collected during 1992-1995 by the CDF experiment. Finding no events that pass our selection, we examine pair production of gluinos (tilde g) and squarks (tilde q) 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(tilde g)>221 GeV/c(2) for M(tilde g) approximately M(tilde q), and M(tilde q)>168 GeV/c(2) for M(tilde q)>>M(tilde g), both with small variation as a function of mu.
