  Planar Josephson junctions provide a versatile platform, alternative to the
nanowire-based geometry, for the generation of the Majorana bound states, due
to the additional phase tunability of the topological superconductivity. The
proximity induction of chiral magnetism and superconductivity in a
two-dimensional electron gas showed remarkable promises to manipulate
topological superconductivity. Here, we consider a Josephson junction involving
a skyrmion crystal and show that the chiral magnetism of the skyrmions can
create and control the Majorana bound states without the requirement of an
intrinsic Rashba spin-orbit coupling. Interestingly, the Majorana bound states
in our geometry are realized robustly at zero phase difference at the junction.
The skyrmion radius, being externally tunable by a magnetic field or a magnetic
anisotropy, brings a unique control feature for the Majorana bound states.
