X-ray line-profile analysis has proved to be the most direct diagnostic of the kinematics and spatial distribution of the very hot plasma around O stars. The Doppler-broadened line profiles provide information about the velocity distribution of the hot plasma, while the wavelength-dependent attenuation across a line profile provides information about the absorption to the hot plasma, thus providing a strong constraint on its physical location. In this paper, we apply several analysis techniques to the emission lines in the Chandra High Energy Transmission Grating Spectrometer (HETGS) spectrum of the late-O supergiant zeta Ori (O9.7 Ib), including the fitting of a simple line-profile model. We show that there is distinct evidence for blueshifts and profile asymmetry, as well as broadening in the X-ray emission lines of zeta Ori. These are the observational hallmarks of a wind-shock X-ray source, and the results for zeta Ori are very similar to those for the earlier O star, zeta Pup, which we have previously shown to be well fit by the same wind-shock line-profile model. The more subtle effects on the line-profile morphologies in zeta Ori, as compared to zeta Pup, are consistent with the somewhat lower density wind in this later O supergiant. In both stars, the wind optical depths required to explain the mildly asymmetric X-ray line profiles imply reductions in the effective opacity of nearly an order of magnitude, which may be explained by some combination of mass-loss rate reduction and large-scale clumping, with its associated porosity-based effects on radiation transfer. In the context of the recent reanalysis of the helium-like line intensity ratios in both zeta Ori and zeta Pup, and also in light of recent work questioning the published mass-loss rates in OB stars, these new results indicate that the X-ray emission from zeta Ori can be understood within the framework of the standard wind-shock scenario for hot stars
