We have carried out high-precision photometry on a large number of archival Hubble Space Telescope images of the Galactic globular cluster NGC 6752, to search for signs of multiple stellar populations. We find a broadened main sequence (MS) and demonstrate that this broadening cannot be attributed either to binaries or to photometric errors. There is also some indication of an MS split. No significant spread could be found along the sub-giant branch, however. Ground-based photometry reveals that in the U versus (U - B) color-magnitude diagram the red-giant branch (RGB) exhibits a clear color spread, which we have been able to correlate with variations in Na and O abundances. In particular, the Na-rich, O-poor stars identified by Carretta et al. define a sequence on the red side of the RGB, while Na-poor, O-rich stars populate a bluer, more dispersed portion of the RGB. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555.