  A significant lower limit on the mass of the lightest neutralino \chi can be
obtained by combining the results from sparticle searches at LEP at
centre-of-mass energies up to 172 GeV with cosmological considerations, if it
is assumed that the \chi is stable. Exclusion domains from slepton searches
close m_\chi \sim 0 loopholes that were left open by previous lower-energy LEP
searches for charginos and neutralinos, leading to the lower limit $m_\chi \ga
17$ GeV. The constraints on supersymmetric parameter space are strengthened
significantly if LEP constraints on supersymmetric Higgs bosons are taken into
account, and further if the relic neutralino density is required to fall within
the range favoured by astrophysics and cosmology. These bounds are considerably
strengthened if universality at the GUT scale is assumed for soft
supersymmetry-breaking scalar masses, including those of the Higgs bosons. In
this case, the Higgs searches play a dramatic role, and we find that m_\chi \ga
40 GeV. Furthermore, we find that if tan\beta \la 1.7 for \mu<0, or tan\beta
\la 1.4 for \mu >0, the cosmological relic density is too large for all values
of m_\chi.
