  A real hypersurface in $\mathbb{C}^2$ is said to be Reinhardt if it is
invariant under the standard $\mathbb{T}^2$-action on $\mathbb{C}^2$. Its CR
geometry can be described in terms of the curvature function of its
``generating curve'', i.e., the logarithmic image of the hypersurface in the
plane $\mathbb{R}^2$. We give a sharp upper bound for the first positive
eigenvalue of the Kohn Laplacian associated to a natural pseudohermitian
structure on a compact and strictly pseudoconvex Reinhardt real hypersurface
having closed generating curve (which amounts to the $\mathbb{T}^2$-action
being free). Our bound is expressed in terms of the $L^2$-norm of the curvature
function of the generating curve and is attained if and only if the curve is a
circle.
