  We define \emph{$0$-shifted} and \emph{$+1$-shifted contact structures} on
differentiable stacks, thus laying the foundations of \emph{shifted Contact
Geometry}. As a side result we show that the kernel of a multiplicative
$1$-form on a Lie groupoid (might not exist as a Lie groupoid but it) always
exists as a differentiable stack, and it is naturally equipped with a stacky
version of the curvature of a distribution. Contact structures on orbifolds
provide examples of $0$-shifted contact structures, while prequantum bundles
over $+1$-shifted symplectic groupoids provide examples of $+1$-shifted contact
structures. Our shifted contact structures are related to shifted symplectic
structures via a Symplectic-to-Contact Dictionary.
