  We study the three-dimensional compressible Navier-Stokes equations coupled
with the $Q$-tensor equation perturbed by a multiplicative stochastic force,
which describes the motion of nematic liquid crystal flows. The local existence
and uniqueness of strong pathwise solution up to a positive stopping time is
established where ``strong" is in both PDE and probability sense. The proof
relies on the Galerkin approximation scheme, stochastic compactness,
identification of the limit, uniqueness and a cutting-off argument. In the
stochastic setting, we develop an extra layer approximation to overcome the
difficulty arising from the stochastic integral while constructing the
approximate solution. Due to the complex structure of the coupled system, the
estimates of the high-order items are also the challenging part in the article.
