Magnetic transmission soft X-ray microscopy has been used to study element-specifically the magnetization reversal behavior of ${(Co_{84}Cr_{16})}_{87}Pt_{l3}$ alloy thin films with a lateral resolution of 35 nm. Our results indicate that the magnetization switching is carried out by a random nucleation process that can be attributed to the reversal of individual grains. We found evidence of a large distribution of the switching fields at the nanogranular length scale, which has to be considered seriously for applications of CoCrPt systems as magnetic high density storage materials.