  The cosmological relic density of the lightest supersymmetric particle of the
minimal supersymmetric standard model is calculated under the assumption of
gauge and Yukawa coupling unification. We employ radiative electroweak breaking
with universal boundary conditions from gravity-mediated supersymmetry
breaking. Coannihilation of the lightest supersymmetric particle, which turns
out to be an almost pure bino, with the next-to-lightest supersymmetric
particle (the lightest stau) is crucial for reducing its relic density to an
acceptable level. Agreement with the mixed or the pure cold (in the presence of
a nonzero cosmological constant) dark matter scenarios for large scale
structure formation in the universe requires that the lightest stau mass is
about 2-8% larger than the bino mass, which can be as low as 222 GeV. The
smallest allowed value of the lightest stau mass turns out to be about 232 GeV.
