  An unstable gravitino with lifetime longer than $10^{26}$ sec or so has been
proposed as a possible dark matter candidate in supergravity models with
R-parity breaking. We find a natural realization of this idea in the minimal
supersymmetric left-right models where left-right symmetry breaking scale in
the few TeV range. It is known that in these models, R-parity must break in
order to have parity breaking as required by low energy weak interactions. The
sub-eV neutrino masses imply that R-parity breaking effects in this model must
be highly suppressed. This in turn makes the gravitino LSP long lived enough,
so that it becomes the dark matter of the Universe. It also allows detectable
displaced vertices at the LHC from NLSP decays. We present a detailed analysis
of the model and some aspects of its rich phenomenology.
