  Neutralino dark matter is generally assumed to be relatively heavy, with a
mass near the electroweak scale. This does not necessarily need to be the case,
however. In the Next-to-Minimal Supersymmetric Standard Model (NMSSM) and other
supersymmetric models with an extended Higgs sector, a very light CP-odd Higgs
boson can naturally arise making it possible for a very light neutralino to
annihilate efficiently enough to avoid being overproduced in the early
Universe.
  In this article, we explore the characteristics of a supersymmetric model
needed to include a very light neutralino, 100 MeV $< \mcnone <$ 20 GeV, using
the NMSSM as a prototype. We discuss the most important constraints from
Upsilon decays, $b \to s \gamma$, $B_s \to \mu^+ \mu^-$ and the magnetic moment
of the muon, and find that a light bino or singlino neutralino is allowed, and
can be generated with the appropriate relic density.
  It has previously been shown that the positive detection of dark matter
claimed by the DAMA collaboration can be reconciled with other direct dark
matter experiments such as CDMS II if the dark matter particle is rather light,
between about 6 and 9 GeV. A singlino or bino-like neutralino could easily fall
within this range of masses within the NMSSM. Additionally, models with sub-GeV
neutralinos may be capable of generating the 511 keV gamma-ray emission
observed from the galactic bulge by the INTEGRAL/SPI experiment.
  We also point out measurements which can be performed immediately at CLEO,
BaBar and Belle using existing data to discover or significantly constrain this
scenario.
