We present a hybrid computational method for simulating the dynamics of macromolecules in solution which couples a mesoscale solver for the fluctuating hydrodynamics (FH) equations with molecular dynamics to describe the macromolecule. The two models interact through a dissipative Stokesian term first introduced by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We show that our method correctly captures the static and dynamical properties of polymer chains as predicted by the Zimm model. In particular, we show that the static conformations are best described when the ratio sigma/b=0.6, where sigma is the Lennard-Jones length parameter and b is the monomer bond length. We also find that the decay of the Rouse modes' autocorrelation function is better described with an analytical correction suggested by Ahlrichs and Dunweg. Our FH solver permits us to treat the fluid equation of state and transport parameters as direct simulation parameters. The expected independence of the chain dynamics on various choices of fluid equation of state and bulk viscosity is recovered, while excellent agreement is found for the temperature and shear viscosity dependence of center of mass diffusion between simulation results and predictions of the Zimm model. We find that Zimm model approximations start to fail when the Schmidt number Sc < or approximately 30. Finally, we investigate the importance of fluid fluctuations and show that using the preaveraged approximation for the hydrodynamic tensor leads to around 3% error in the diffusion coefficient for a polymer chain when the fluid discretization size is greater than 50 A.