The spectrum of excitations of the chiral superconducting ring with internal and external radii Ri, Re (comparable with coherence length ξ) trapping a unit flux Φ0 is calculated. We find within the Bogoliubov-de Gennes approach that there exists a pair of precisely zero-energy states when 2k⊥ (Re - R i)/π is integer (here k⊥ is the momentum component in the disk plane while k⊥ξ > 1). 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.