Based on density functional theory (DFT) calculations, we predict that monolayer of OsCl3 (which is 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 inplane easy-axis. The band gap opened by SOC is Eg ≃ 67 meV (or ≃ 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 anisotropic planar rotator ferromagnet is TC 350 K. The Chern number C = −1, generated by the manifold of Os t2g 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 both strong SOC and moderate correlation effects, we employ DFT+U calculations to show how increasing on-site Coulomb repulsion U : gradually reduces Eg while maintaining C = −1 for 0 < U < Uc; leads to metallic phase with Eg = 0 at Uc; and opens a gap of topologically trivial Mott insulating phase with C = 0 for U > Uc.