  In this note we propose the generalization of the notion of a holomorphic
contact structure on a manifold (smooth variety) to varieties with rational
singularities and prove basic properties of such objects. Natural examples of
singular contact varieties come from the theory of nilpotent orbits: every
projectivization of the closure of a nilpotent orbit in a semisimple Lie
algebra satisfies our definition after normalization. We show the
correspondence between symplectic varieties with the structure of a
$\mathbb{C}^*$-bundle and the contact ones along with the existence of the
stratification \`a la Kaledin. In the projective case we demonstrate the
equivalence between crepant and contact resolutions of singularities, show the
uniruledness and give a full classification of projective contact varieties in
dimension 3.
