  We characterize the energy transport in a one dimensional $\mathbb{Z}_3$
chiral clock model. The model generalizes the $\mathbb{Z}_2$ symmetric
transverse field Ising model (TFIM). The model is parametrized by a chirality
parameter $\theta$, in addition to $f$ and $J$ which are analogous to the
transverse field and the nearest neighbour spin coupling in the TFIM. Unlike
the well studied TFIM and XYZ models, does not transform to a fermionic system.
We use a matrix product states implementation of the Lindblad master equation
to obtain the non-equilibrium steady state (NESS) in systems of sizes up to
$48$. We present the estimated NESS current and its scaling exponent $\gamma$
as a function of $\theta$ at different $f/J$. The estimated
$\gamma(f/J,\theta)$ point to a ballistic energy transport along a line of
integrable points $f=J\cos{3\theta}$ in the parameter space; all other points
deviate from ballistic transport. Analysis of finite size effects within the
available system sizes suggest a diffusive behavior away from the integrable
points.

Statistical Mechanics;Disordered Systems and Neural Networks