The molecular polarization in a 1,3-dimethylimidazolium chloride ([DMIM][Cl]) ionic liquid is analyzed for a bulk liquid via the Car-Parrinello approach. The analysis reveals that the electric dipole moments of cations and anions are characterized by large fluctuations, however these are primarily due to the molecules in the immediate surroundings. These results on one hand shed light on some basic physical and chemical features of this liquid, and on the other represent a fundamental handle for the development of accurate classical force fields; this aspect is extensively discussed and some suggestions are made.