  We discuss a new variant of the E6 inspired supersymmetric standard model
(E6SSM) in which the two inert singlinos are exactly massless and the dark
matter candidate has a dominant bino component. A successful relic density is
achieved via a novel mechanism in which the bino scatters inelastically into
heavier inert Higgsinos during the time of thermal freeze-out. The two massless
inert singlinos contribute to the effective number of neutrino species at the
time of Big Bang Nucleosynthesis, where the precise contribution depends on the
mass of the Z' which keeps them in equilibrium. For example for mZ' > 1300 GeV
we find Neff \approx 3.2, where the smallness of the additional contribution is
due to entropy dilution. We study a few benchmark points in the constrained
E6SSM with massless inert singlinos to illustrate this new scenario.
