  Presented is the theory of thermal Hall conductivity $\kappa_{xy}$ in the
vortex state of high temperature cuprate superconductors in the clean limit. We
show that $\lim_{T \to 0} \kappa_{xy}/T$ is a {\em staircase} function of 1/B
with an envelope that scales as 1/B. The relation to the experiments is
discussed.
