  Atomically flat semiconducting materials such as monolayer WSe$_2$ hold great
promise for novel optoelectronic devices. Recently, quantum light emission has
been observed from bound excitons in exfoliated WSe$_2$. As part of developing
optoelectronic devices, the control of the radiative properties of such
emitters is an important step. Here we report the coupling of a bound exciton
in WSe$_2$ to open microcavities. We use a range of radii of curvature in the
plano-concave cavity geometry with mode volumes in the $\lambda^3$ regime,
giving Purcell factors of up to 8 while increasing the photon flux five-fold.
Additionally we determine the quantum efficiency of the single photon emitter
to be $\eta = 0.46 \pm 0.03$. Our findings pave the way to cavity-enhanced
monolayer based single photon sources for a wide range of applications in
nanophotonics and quantum information technologies.
