The major core helium-burning flash in a low-mass Population III model of zero initial metallicity (Z = 0) begins far off center, near a region where hydrogen remains at high abundance. During the flash, convection extends outward from the region of maximum energy generation (by helium-burning reactions) into the inner tail of the hydrogen profile. Hydrogen migrates inward into the convective shell and, in the region where the time scale for proton capture on 12C becomes small compared with the time scale for further inward migration, a hydrogen shell flash is initiated. The overall rate of energy production by CN-cycle reactions increases exponentially with time, and when the hydrogen-burning luminosity begins to exceed the helium-burning luminosity, energy flows inward from the region of most intense hydrogen burning, causing the convective shell to split into two convective shells which are separated by a region within which energy flows inward by radiative diffusion. The outer convective shell contains hydrogen, 12C, and the products of CN-cycle burning. After both nuclear-burning flashes have died down, convection driven by helium burning ceases, while the convective shell containing a large abundance of hydrogen and CN-cycle isotopes persists. As stored energy from the hydrogen flash escapes the stellar interior, this hydrogen-rich, CN-enhanced convective shell merges with the convective envelope, temporarily transforming the Z = 0 model star into an object whose surface is CNO-enhanced (XCNO ≈ 0.0002). As stored energy from the helium flash escapes the interior at a slightly later time, additional CN-enhanced material is dredged up to the stellar surface. This creates an object that is CNO-rich (XCNO ≈ 0.004), but still devoid of Fe, unlike any star yet discovered. On the other hand, big bang nucleosynthesis actually produces heavy elements to the extent that a more realistic Population III model star should be characterized by an initial metallicity of Z ∼ 10-10, and accretion from the interstellar medium will increase the metallicity beyond this. It is possible that a low-mass model characterized by this more realistic choice of Z will, as a consequence of the core helium flash, develop characteristics intermediate between those predicted by our Z = 0 model and models with Z ≥ 10-4, which do not mix to the surface isotopes produced in the interior. Our next goal is to explore this possibility, with the hope that we can assess whether or not a star such as CD - 38°245, currently with [Fe/H] = -4.5, might be a Population III star modified by internal nucleosynthesis and mixing, as well as by accretion.