We have obtained a very deep exposure (813 ks) of ζ Puppis (O4 supergiant) with the Chandra HETG Spectrometer. Here we report on analysis of the 1-9 Å region, especially well suited for Chandra, which has a significant contribution from continuum emission between well separated emission lines from high-ionization species. These data allow us to study the hottest plasma present through the continuum shape and emission line strengths. Assuming a power-law emission measure distribution that has a high-temperature cutoff, we find that the emission is consistent with a thermal spectrum having a maximum temperature of 12 MK as determined from the corresponding spectral cutoff. This implies an effective wind shock velocity of 900 km s-1, well below the wind terminal speed of 2250 km s-1. For X-ray emission that forms close to the star, the speed and X-ray flux are larger than can be easily reconciled with strictly self-excited line-deshadowing-instability models, suggesting a need for a fraction of the wind to be accelerated extremely rapidly right from the base. This is not so much a dynamical instability as a nonlinear response to changing boundary conditions.