The spectrum of excitations of the chiral superconducting ring with internal
and external radii, comparable with coherence length, trapping a unit flux is
calculated. We find within the Bogoliubov-deGennes approach that there exists a
pair of precisely zero energy states. They are not protected by topology, but
are stable under certain deformations of the system. We discuss the ways to
tune the system so that it grows into such a "Majorana disk". This condition
has a character of a resonance phenomenon
