We calculate expected event rates for direct detection of relic neutralinos
as a function of parameter space of the minimal supergravity model. Numerical
results are presented for the specific case of a 73Ge detector. We find
significant detection rates (R>0.01 events/kg/day) in regions of parameter
space most favored by constraints from B→Xsγ and the cosmological
relic density of neutralinos. The detection rates are especially large in
regions of large tanβ, where many conventional signals for supersymmetry
at collider experiments are difficult to detect. If the parameter tanβ
is large, then there is a significant probability that the first direct
evidence for supersymmetry could come from direct detection experiments, rather
than from collider searches for sparticles.Comment: 25 page REVTEX file including 9 PS figure