The role of chlorine doping in CH3NH3PbI3 represents an important open issue in the use of hybrid perovskites for photovoltaic applications. In particular, even if a positive role of chlorine doping on perovskite film formation and on material morphology has been demonstrated, an inherent positive effect on the electronic and photovoltaic properties cannot be excluded. Here we carried out periodic density functional theory and Car-Parrinello molecular dynamics simulations, going down to similar to 1% doping, to investigate the effect of chlorine on CH3NH3PbI3. We found that such a small doping has important effects on the dynamics of the crystalline structure, both with respect to the inorganic framework and with respect to the cation libration motion. Together, we observe a dynamic spatial localization of the valence and conduction states in separated spatial material regions, which takes place in the 10(-1) ps time scale and which could be the key to ease of exciton dissociation and, likely, to small charge recombination in hybrid perovskites. Moreover, such localization is enhanced by chlorine doping, demonstrating an inherent positive role of chlorine doping on the electronic properties of this class of materials.