  Carrying information using generation and detection of the orbital current,
instead of the spin current, is an emerging field of research, where the
orbital Hall effect (OHE) is an important ingredient. Here, we propose a new
mechanism of the OHE that occurs in {\it non-}centrosymmetric materials. We
show that the broken inversion symmetry in the 2D transition metal
dichalcogenides (TMDCs) causes a robust orbital moment, which flow in different
directions due to the opposite Berry curvatures under an applied electric
field, leading to a large OHE. This is in complete contrast to the
inversion-symmetric systems, where the orbital moment is induced only by the
external electric field. We show that the valley-orbital locking as well as the
OHE both appear even in the absence of the spin-orbit coupling. The non-zero
spin-orbit coupling leads to the well-known valley-spin locking and the spin
Hall effect, which we find to be weak, making the TMDCs particularly suitable
for direct observation of the OHE, with potential application in {\it
orbitronics}.
