  The Kitaev quantum spin liquid displays the fractionalization of quantum
spins into Majorana fermions. The emergent Majorana edge current is predicted
to manifest itself in the form of a finite thermal Hall effect, a feature
commonly discussed in topological superconductors. Here we report on thermal
Hall conductivity $\kappa_{xy}$ measurements in $\alpha$-RuCl$_3$, a candidate
Kitaev magnet with the two-dimensional honeycomb lattice. In a spin-liquid
(Kitaev paramagnetic) state below the temperature characterized by the Kitaev
interaction $J_K/k_B \sim 80$ K, positive $\kappa_{xy}$ develops gradually upon
cooling, demonstrating the presence of highly unusual itinerant excitations.
Although the zero-temperature property is masked by the magnetic ordering at
$T_N=7$ K, the sign, magnitude, and $T$-dependence of $\kappa_{xy}/T$ at
intermediate temperatures follows the predicted trend of the itinerant Majorana
excitations.
