  Transition metal dichalcogenides have a rich exciton landscape consisting of
a variety of bright and dark excitonic states. We consider the lowest-energy
dark states in $\hbox{MoS}_2$, which can be referred to as hybrid excitons, as
they are formed by a Dirac electron and a Schr\"{o}dinger hole. The chiral
nature of the Dirac electron introduces asymmetry to the excited exciton state
spectrum and entangles the relative motion of the electron and hole with the
center-of-mass motion. We demonstrate that the entanglement generates an
additional contribution to the Berry curvature of hybrid excitons. The
additional contribution is substrate-dependent and accounts for almost one
quarter of the Berry curvature in suspended samples. The nontrivial geometry of
hybrid excitons is manifested in the optical anomalous valley Hall effect,
which can be observed via recently developed pump-probe photoemission
spectroscopy. We argue that the Hall angle of hybrid excitons is approximately
one half of that for bright excitons. Moreover, the anticipated long lifetime
of hybrid excitons favors an extended propagation distance and allows the
spatial separation of hybrid excitons with different valley indices.
