gamma Cas is the prototypical classical B0.5e star and is now known to be the primary in a wide binary system. It has long been famous for its unique hard X-ray characteristics, among which are variations that correlate with changes in a number of optical light and UV line and continuum properties. These peculiarities have led to a picture in which processes on or near the Be star produce the observed X-ray emission. In this paper we report on a 53 ks Chandra High Energy Transmission Grating Spectrometer observation of this target. An inspection of our spectrum shows that it is quite atypical for a massive star. The emission lines appear weak because of a strong short-wavelength continuum that arises from a hot plasma with kT = 11-12 keV. The spectrum exhibits many lines, the strongest of which are Lyalpha features of H-like species from Fe through the even-Z intermediate elements (S, Si, Mg, and Ne), down to O and N. Line ratios of the rif triplet for a variety of He-like ions and of Fe XVII are consistent with the dominance of collisional atomic processes. However, the presence of Fe and Si fluorescence K features indicates that photoionization also occurs in nearby cold gas. The line profiles indicate a mean velocity at rest with an rms line broadening of 500 km s(-1) and little or no asymmetry. An empirical global-fitting analysis of the line and continuum spectrum suggests that there are actually three or four plasma emission components. The first is the dominant hot ( 12 keV) component, of which some fraction (10%-30%) is heavily absorbed, while the remainder is affected by a much lower column density of only 3 x 10(21) cm(-2). The hot component has a Fe abundance of only 0.22 +/- 0.05 solar. The other two or three major emission components are warm and are responsible for most other emission lines. These components are dominated by plasma having temperatures near 0.1, 0.4, and 3 keV. Altogether, the warm components have an emission measure of about 14% of the hot component, a low column density, and a more nearly solar composition. The 100 eV component is consistent with X-ray temperatures associated with a wind in a typical early B star. Nonetheless, its emission measure is a few times higher than would be expected from this explanation. The strength of the fluorescence features and the dual-column absorption model for the hot plasma component suggest the presence near the hot sites of a cold gas structure with a column density of similar to10(23) cm(-2). Because this is also the value determined by Millar and Marlborough for the vertical column of the Be disk of gamma Cas, these attributes suggest that the X-ray emitting sources could be close to the disk and hence to the Be star. Finally, we discuss the probably related issues of the origin of the warm emission components, as well as the puzzling deficient Fe abundance in the hot component. It is possible that the latter anomaly is related to the FIP (abundance fractionation) effect found in certain coronal structures on the Sun and RS CVn stars. This would be yet another indication that the X-rays are produced in the immediate vicinity of the Be star