  We study the Navier-Stokes system describing the motion of a compressible
viscous fluid driven by a nonlinear multiplicative stochastic force. We
establish local in time existence (up to a positive stopping time) of a unique
solution, which is strong in both PDE and probabilistic sense. Our approach
relies on rewriting the problem as a symmetric hyperbolic system augmented by
partial diffusion, which is solved via a suitable approximation procedure using
the stochastic compactness method and the Yamada-Watanabe type argument based
on the Gy\"ongy-Krylov characterization of convergence in probability. This
leads to the existence of a strong (in the PDE sense) pathwise solution.
Finally, we use various stopping time arguments to establish the local
existence of a unique strong solution to the original problem.
