  We propose a realization of chiral Majorana modes propagating on the hinges
of a 3D antiferromagnetic topological insulator, which was recently
theoretically predicted and experimentally confirmed in the tetradymite-type
$\mathrm{MnBi_2Te_4}$-related ternary chalgogenides. These materials consist of
ferromagnetically ordered 2D layers, whose magnetization direction alternates
between neighboring layers, forming an antiferromagnetic order. Besides
surfaces with a magnetic gap, there also exsist gapless surfaces with a single
Dirac cone, which can be gapped out when proximity coupled to an $s$-wave
superconductor. On the sharing edges between the two types of gapped surfaces,
the chiral Majorana modes emerge. We further propose experimental signatures of
these Majoana hinge modes in terms of two-terminal conductance measurements.
