  We obtain necessary and sufficient conditions for an initial data set for the
vacuum conformal Einstein field equations to give rise to a spacetime
development in possession of a Killing spinor. The fact that the conformal
Einstein field equations are used in our derivation allows for the possibility
of the initial hypersurface $\mathcal{S}$ intersecting non-trivially with (or
even being a subset of) null infinity $\mathscr{I}$. For conciseness, these
conditions are derived assuming that the initial hypersurface is spacelike.
Hence, in particular, these conformal Killing spinor initial data equations
encode necessary and sufficient conditions for the existence of a Killing
spinor in the development of asymptotic initial data on spacelike components of
$\mathscr{I}$.
