  We identify a valley-polarized Chern insulator in the van der Waals
heterostructure, Pt$_{2}$HgSe$_{3}$/CrI$_3$, for potential applications with
interplay between electric, magnetic, optical, and mechanical effects. The
interlayer proximity magnetic coupling nearly closes the band gap of
Pt$_{2}$HgSe$_{3}$ and the strong intra-layer spin-orbit coupling further lifts
the valley degeneracy by over 100 meV leading to positive and negative band
gaps at opposite valleys. In the valley with negative gap, the interfacial
Rashba spin-orbit coupling opens a topological band gap of 17.8 meV, which is
enlarged to 30.8 meV by adding an $h$-BN layer. We find large orbital
magnetization in Pt$_{2}$HgSe$_{3}$ layer that is much larger than spin, which
can induce measurable optical Kerr effect. The valley polarization and Chern
number are coupled to the magnetic order of the nearest neighboring CrI$_3$
layer, which is switchable by electric, magnetic, and mechanical means in
experiments. The presence of $h$-BN protects the topological phase allowing the
construction of superlattices with valley, spin, and layer degrees of freedoms.
