  We study properties of the lightest neutralino (\chi) and calculate its
cosmological relic density in a supersymmetric U(1)' model with a secluded
U(1)' breaking sector (the S-model). The lightest neutralino mass is smaller
than in the minimal supersymmetric standard model; for instance, m_\chi < 100
GeV in the limit that the U(1)' gaugino mass is large compared to the
electroweak scale. We find that the Z-\chi-\chi coupling can be enhanced due to
the singlino components in the extended neutralino sector. Neutralino
annihilation through the Z-resonance then reproduces the measured cold dark
matter density over broad regions of the model parameter space.
