  We study supersymmetric extension of the Einstein-aether gravitational model
where local Lorentz invariance is broken down to the subgroup of spatial
rotations by a vacuum expectation value of a timelike vector field called
aether. Embedding aether into a chiral vector superfield, we construct the most
general action which describes dynamics of linear perturbations around the
Lorentz-violating vacuum and is invariant under the linearized supergravity
transformations. The analysis is performed both in the off-shell non-minimal
superfield formulation of supergravity and in the "on-shell" approach invoking
only physical component fields. The resulting model contains a single free
coupling, in addition to the standard supergravity parameters. The spectrum of
physical excitations features an enhanced on-shell gravity multiplet comprising
four states with helicities 2, 3/2, 3/2 and 1 propagating with superluminal
velocity. The remaining excitations propagate with the speed of light. We
outline the observational constraints on the model following from its
low-energy phenomenology.
