It has been suggested by Groot Nibbelink and Pospelov that Lorentz invariance can be an emergent symmetry of low-energy physics provided the theory enjoys a non-relativistic version of supersymmetry. We construct a model that realizes the latter symmetry dynamically: it breaks Lorentz invariance but leaves the supersymmetry generators intact. The model is a supersymmetric extension of the dynamical aether theory of Jacobson and Mattingly in fixed flat spacetime. It exhibits rich dynamics and possesses a family of inequivalent vacua realizing different symmetry breaking patterns. In particular, we find stable vacua that break spontaneously spatial isotropy. Supersymmetry breaking terms give masses to fermionic and bosonic partners of the aether field. We comment on the coupling of the model to supergravity and on the implications for Hořava gravity.