We present an overview of four phase-constrained Chandra HETGS X-ray observations of Delta Ori A. Delta Ori A is actually a triple system which includes the nearest massive eclipsing spectroscopic binary, Delta Ori Aa, the only such object which can be observed with little phase-smearing with the Chandra gratings. Since the fainter star, Delta Ori Aa2, has a much lower X-ray luminosity than the brighter primary, Delta Ori A provides a unique system with which to test the spatial distribution of the X-ray emitting gas around Delta Ori Aa1 via occultation by the photosphere of and wind cavity around the X-ray dark secondary. Here we discuss the X-ray spectrum and X-ray line profiles for the combined observation, having an exposure time of nearly 500 ksec and covering nearly the entire binary orbit. Companion papers discuss the X-ray variability seen in the Chandra spectra, present new space-based photometry and ground-based radial velocities simultaneous with the X-ray data to better constrain the system parameters, and model the effects of X-rays on the optical and UV spectrum. We find that the X-ray emission is dominated by embedded wind shock emission from star Aa1, with little contribution from the tertiary star Ab or the shocked gas produced by the collision of the wind of Aa1 against the surface of Aa2. We find a similar temperature distribution to previous X-ray spectrum analyses. We also show that the line half-widths are about $0.3-0.5times$ the terminal velocity of the wind of star Aa1. We find a strong anti-correlation between line widths and the line excitation energy, which suggests that longer-wavelength, lower-temperature lines form farther out in the wind. Our analysis also indicates that the ratio of the intensities of the strong and weak lines of ion{Fe}{17} and ion{Ne}{10} are inconsistent with model predictions, which may be an effect of resonance scattering
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