  A distinct thermal Hall signal is observed in a quantum spin liquid candidate
Ba$_3$CuSb$_2$O$_9$. The transverse thermal conduction shows a power-law
temperature dependence below 40 K where a spin gap opens. We suggest that,
through the very low longitudinal thermal conductivity and the thermal Hall
signals, a phonon Hall effect is induced by strong phonon scatterings by orphan
Cu$^{2+}$ spins formed in random domains of Cu$^{2+}$-Sb$^{5+}$ dumbbells.
