[en] Motivated by Sr₂RuO₄, we consider a chiral superconductor where the gap is strongly suppressed along certain momentum directions. We evaluate the thermal Hall conductivity in the gapless regime, i.e., at low temperature compared with the impurity band width γ, taking the simplest model of isotropic impurity scattering. We find that, under favorable circumstances, this thermal Hall conductivity can be quite significant and is smaller than the diagonal component (the universal thermal conductivity) only by a factor of $1/\mathrm{l}\mathrm{n}(2{\mathrm{\Delta <!--\; ??\; -->}}_M/\mathrm{\gamma <!--\; ??\; -->})$, where ${\mathrm{\Delta <!--\; ??\; -->}}_M$ is the maximum gap. (paper)