  $\alpha$-RuCl$_3$ is a Mott insulator with a honeycomb lattice with strong
spin-orbit coupling. We report dielectric measurements on $\alpha$-RuCl$_3$
single crystals under field. At zero field, the dielectric constant,
$\epsilon$, drops rapidly when cooled through the magnetic transition
temperature T$_N$. With increasing field, the onset of the drop in $\epsilon$
tracks the T$_N$. Such behavior is absent with field above a critical value
H$_c$ ~ 7.5 T, indicating the onset of a quantum phase transition. Our data
suggest that the dielectric constant can be used as a probe of magnetic
ordering in $\alpha$-RuCl$_3$, and $\alpha$-RuCl$_3$ is a possible type-II
multiferroics.
