Following pioneering works, the 3D hybrid lead-halide perovskites CH3NH3PbX3 (X=Cl, Br, I) have recently been shown to drastically improve the efficiency of Dye Sensitized Solar Cells (DSSC). It is predicted to open "a new era and a new avenue of research and development for low-cost solar cells ... likely to push the absolute power conversion efficiency toward that of CIGS (20%) and then toward and beyond that of crystalline silicon (25%)" (Snaith, H. J. Phys Chem. Lett. 4, 3623-3630 (2013).). Here, we investigate theoretically the crystalline phases of one of the hybrids relevant for photovoltaic applications, namely CH3NH3PbCl3. Critical electronic states and optical absorption are thoroughly investigated both in the low and high temperature phases. Our findings reveal the dramatic effect of spin orbit coupling on their multiple band gaps. Their physical properties are compared to those of conventional semiconductors, evidencing inversion of band edge states.