  Tellurium is a high-performance thermoelectric material due to its superior
electronic transport and low lattice thermal conductivity ($\kappa_L$). Here,
we report the ultralow $\kappa_L$ in the monolayer tellurium, i.e., tellurene,
which has been successfully synthesized in recent experiments. We find
tellurene has a compellingly low room temperature $\kappa_L$ of 2.16 and 4.08 W
m$^{-1}$ K$^{-1}$ along the armchair and zigzag directions, respectively, which
is lower than any reported values for other 2D materials. We attribute this
unusually low $\kappa_L$ to the soft acoustic modes, extremely low-energy
optical modes and the strong scattering among optical-acoustic phonons, which
place tellurene as a potential novel thermoelectric material. Finally, we
disclose that $\kappa_L$ is proportional to the largest acoustic phonon
frequency ($\omega_{D}^{a}$) and the lowest optical phonon frequency at
$\Gamma$ point ($\omega_{\Gamma}^{o}$) in 2D materials, which reflect both
harmonic and anharmonic thermal properties respectively.
