  Using {\it ab initio} density functional theory, here we systematically study
the monolayer MoOCl$_2$ with a $4d^2$ electronic configuration. Our main
results is that an orbital-selective Peierls phase (OSPP) develops in
MoOCl$_2$, resulting in the dimerization of the Mo chain along the $b$-axis.
Specifically, the Mo-$d_{xy}$ orbitals form robust molecular-orbital states
inducing localized $d_{xy}$ singlet dimers, while the Mo-$d_{xz/yz}$ orbitals
remain delocalized and itinerant. Our study shows that MoOCl$_2$ is globally
metallic, with the Mo-$d_{xy}$ orbital bonding-antibonding splittings opening a
gap and the Mo-$d_{xz/yz}$ orbitals contributing to the metallic conductivity.
Overall, the results resemble the recently much discussed orbital-selective
Mott phase but with the localized band induced by a Peierls distortion instead
of Hubbard interactions. Finally, we also qualitatively discuss the possibility
of OSPP in the $3d^2$ configuration, as in CrOCl$_2$.
