  Based on density functional theory (DFT) calculations, we predict that a
monolayer of OsCl$_3$---a layered material whose interlayer coupling is weaker
than in graphite---possesses a quantum anomalous Hall (QAH) insulating phase
generated by the combination of honeycomb lattice of osmium atoms, their strong
spin-orbit coupling (SOC) and ferromagnetic ground state with {\em in-plane}
easy-axis. The band gap opened by SOC is \mbox{$E_g \simeq 67$ meV} (or
\mbox{$\simeq 191$ meV} if the easy-axis can be tilted out of the plane by an
external electric field), and the estimated Curie temperature of such {\em
anisotropic planar rotator} ferromagnet is $T_\mathrm{C} \lesssim 350$ K. The
Chern number $\mathcal{C}=-1$, generated by the manifold of Os $t_{2g}$ bands
crossing the Fermi energy, signifies the presence of a single chiral edge state
in nanoribbons of finite width, where we further show that edge states are
spatially narrower for zigzag than armchair edges and investigate edge-state
transport in the presence of vacancies at Os sites. Since $5d$ electrons of Os
exhibit {\em both} strong SOC and moderate correlation effects, we employ DFT+U
calculations to show how increasing on-site Coulomb repulsion $U$: gradually
reduces $E_g$ while maintaining $\mathcal{C} = -1$ for $0 < U < U_c$; leads to
metallic phase with $E_g = 0$ at $U_c$; and opens the gap of topologically
trivial Mott insulating phase with $\mathcal{C}=0$ for $U > U_c$.
