We address the question of how light the lightest supersymmetric parti
cle neutralino can be to be a reliable cold dark matter (CDM) particle
candidate. To this end we perform a combined analysis of the paramete
r space of the minimal supersymmetric standard model (MSSM) taking int
o account cosmological and accelerator constraints including those fro
m the radiative b-->s gamma decay. Appropriate grand unification (GUT)
scenarios are considered. We find that the relaxation of gaugino mass
unification is sufficient to obtain a phenomenologically and cosmolog
ically viable solution of the MSSM with a neutralino as light as 3 GeV
. We find good prospects for the direct detection of these superlight
CDM neutralinos via elastic scattering off various nuclei in:the forth
coming experiments with low-threshold DM detectors. In a certain sense
, these experiments can probe the gaugino mass unification giving cons
traints on the possible GUT scenarios within the MSSM.