We report on the linear optical properties of the chiral magnet Cu2OSeO3, specifically associated with the absence of inversion symmetry, the chiral crystallographic structure, and magnetic order. Through spectroscopic ellipsometry, we observe local crystal-field excitations below the charge-transfer gap. These crystal-field excitations are optically allowed due to the lack of inversion symmetry at the Cu sites. Optical polarization rotation measurements were used to study the structural chirality and magnetic order. The temperature dependence of the natural optical rotation, originating in the chiral crystal structure, provides evidence for a finite magneto-electric effect in the helimagnetic phase. We find a large magneto-optical susceptibility on the order of V(540nm)~10^4 rad/(T*m) in the helimagnetic phase and a maximum Faraday rotation of ~165deg/mm in the ferrimagnetic phase. The large value of V can be explained by considering spin cluster formation and the relative ease of domain reorientation in this metamagnetic material. The magneto-optical activity allows us to map the magnetic phase diagram, including the skyrmion lattice phase. In addition to this, we probe and discuss the nature of the various magnetic phase transitions in Cu2OSeO3.