  The underlying mechanism of the thermal Hall effect (THE) generated by
phonons in a variety of insulators is yet to be identified. Here, we report on
a sizeable thermal Hall conductivity in NiPS$_3$, a van de Waals stack of
honeycomb layers with a zigzag antiferromagnetic order below $T_N$ = 155 K. The
longitudinal ($\kappa_{aa}$) and the transverse ($\kappa_{ab}$) thermal
conductivities peak at the same temperature and the thermal Hall angle
($\kappa_{ab}/\kappa_{aa}/B$) respects a previously identified bound. The
amplitude of $\kappa_{ab}$ is extremely sensitive to the amplitude of
magnetization along the $b$-axis, in contrast to the phonon mean free path,
which is not at all. We show that the magnon and acoustic phonon bands cross
each other along the $b^\ast$ orientation in the momentum space. The
exponential temperature dependence of $\kappa_{ab}$ above its peak reveals an
energy scale on the order of magnitude of the gap expected to be opened by
magnon-phonon hybridization. This points to an intrinsic scenario for THE with
possible relevance to other magnetic insulators.
