The CRESST-II cryogenic Dark Matter search, aiming at detection of WIMPs via elastic scattering off nuclei in CaWO 4 crystals, completed 730 kg days of data taking in 2011. We present the data collected with eight detector modules, each with a two-channel readout; one for a phonon signal and the other for coincidently produced scintillation light. The former provides a precise measure of the energy deposited by an interaction, and the ratio of scintillation light to deposited energy can be used to discriminate different types of interacting particles and thus to distinguish possible signal events from the dominant backgrounds. Sixty-seven events are found in the acceptance region where a WIMP signal in the form of low energy nuclear recoils would be expected. We estimate background contributions to this observation from four sources: (1) “leakage” from the e / γ -band (2) “leakage” from the α -particle band (3) neutrons and (4)  206 Pb recoils from 210 Po decay. Using a maximum likelihood analysis, we find, at a statistical significance of more than 4 σ , that these sources alone are not sufficient to explain the data. The addition of a signal due to scattering of relatively light WIMPs could account for this discrepancy, and we determine the associated WIMP parameters.