Multi-band Hubble Space Telescope photometry reveals that the main sequence, sub-giant, and the red-giant branch of the globular cluster NGC 6752 splits into three main components in close analogy with the three distinct segments along its horizontal branch stars. These triple sequences are consistent with three stellar groups: a stellar population with a chemical composition similar to field-halo stars (Population a), a Population (c) with enhanced sodium and nitrogen, depleted carbon and oxygen, and an enhanced helium abundance (ΔY ~ 0.03), and a Population (b) with an intermediate (between Populations a and c) chemical composition and slightly enhanced helium (ΔY ~ 0.01). These components contain ~25% (Population a), ~45% (Population b), and ~30% (Population c) of the stars. No radial gradient for the relative numbers of the three populations has been identified out to about 2.5 half-mass radii. 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.