The effects of molecular fluctuations on chemical oscillations and chaos are investigated. The calculations are carried out using a reactive lattice-gas automaton which provides a mesoscopic description of the reactive dynamics. A specific chemical model, the Willamowski-Rossler reaction, is used to illustrate the effects. The applicability of mass-action rate laws and reaction-diffusion equations are considered and the character of the fluctuations in various dynamical regimes for both spatially-distributed and spatially-homogeneous systems are examined. The work provides information on the molecular origin of macroscopic, self-organized structures in far-from-equilibrium reacting systems.