  The honeycomb Kitaev model in a magnetic field is a source of a topological
quantum spin liquid with Majorana fermions and gauge flux excitations as
fractional quasiparticles. We present experimental results for the thermal Hall
effect of the material $\alpha$-RuCl$_{3}$ which recently emerged as a prime
candidate for realizing such physics. At temperatures above long-range magnetic
ordering $T\gtrsim T_N\approx8$ K, we observe with an applied magnetic field
$B$ perpendicular to the honeycomb layers a sizeable positive transversal heat
conductivity $\kappa_{xy}$ which increases linearly with $B$. Upon raising the
temperature, $\kappa_{xy}(T)$ increases strongly, exhibits a broad maximum at
around 30 K, and eventually becomes negligible at $T\gtrsim 125$ K. Remarkably,
the longitudinal heat conductivity $\kappa_{xx}(T)$ exhibits a sizeable
positive thermal magnetoresistance effect. Thus, our findings provide clear-cut
evidence for longitudinal and transverse magnetic heat transport and underpin
the unconventional nature of the quasiparticles in the paramagnetic phase of
$\alpha$-RuCl$_{3}$.
