LEP and radiative electroweak breaking close the light gluino window

We show that the LEP lower bound on the chargino mass, in conjunction with the well motivated theoretical requirement of radiative electroweak symmetry breaking, imply an upper bound on the lightest Higgs boson mass ($m_h\lsim62\GeV$) in a supersymmetry breaking scenario where the gluino mass is a few GeV. Moreover, Higgs searches at LEP in the context of this model require $m_h\gsim61\GeV$. The remaining experimentally allowed region in the five-dimensional parameter space of this light gluino model is severely fine-tuned (with $\tan\beta=1.88-1.89$ and $m_t=114.0-114.3\GeV$) and cosmologically troublesome (with a neutralino relic abundance over {\it five-hundred times larger than allowed}). Modest improvements in sensitivity in LEP Higgs searches and Tevatron top-quark searches should soon exclude this theoretically disfavored model completely.