  We report Chern insulating phases emerging from a single layer of layered
chalcogenide CrSiTe$_{3}$, a transition metal trichacogenides (TMTC) material,
in the presence of charge doping. Due to strong hybridization with Te $p$
orbitals, the spin-orbit coupling effect opens a finite band gap, leading to a
nontrivial topology of the Cr $e_{\mathrm{g}}$ conduction band manifold with
higher Chern numbers. Our calculations show that quantum anomalous Hall effects
can be realized by adding one electron in a formula unit cell of
Cr$_{2}$Si$_{2}$Te$_{6}$, equivalent to electron doping by
2.36$\times$10$^{14}$ cm$^{-2}$ carrier density. Furthermore, the
doping-induced anomalous Hall conductivity can be controlled by an external
magnetic field via spin-orientation-dependent tuning of the spin-orbit
coupling. In addition, we find distinct quantum anomalous Hall phases employing
tight-binding model analysis, suggesting that CrSiTe$_{3}$ can be a fascinating
new platform to realize Chern insulating systems with higher Chern numbers.
