The Cyg OB2 association contains some of the most luminous OB stars in our Galaxy, the brightest of which are also among the most luminous in X-rays. We obtained a Chandra High Energy Transmission Grating Spectrometer observation centered on Cyg OB2 No. 8A, the most luminous X-ray source in the association. Although our analysis focuses on the X-ray properties of Cyg OB2 No. 8A, we also present limited analyses of three other OB stars (Cyg OB2 Nos. 5, 9, and 12). Applying standard diagnostic techniques as used in previous studies of early-type stars, we find that the X-ray properties of Cyg OB2 No. 8A are very similar to those of other OB stars that have been observed using high-resolution X-ray spectroscopy. From analyses of the He-like ion fir emission lines (Mg XI, Si XIII, S XV, and Ar XVII), we derive radial distances of the He-like line emission sources and find that the higher energy ions have their lines form closer to the stellar surface than those of lower ion states. These fir-inferred radii are also found to be consistent with their corresponding X-ray continuum optical depth unity radii. Both of these findings are in agreement with previous O star studies and again suggest that anomalously strong shocks or high-temperature zones may be present near the base of the wind. The observed X-ray emission-line widths (HWHM ~ 1000 km s-1) are also compatible with the observations of other O star supergiants. Since Cyg OB2 No. 8A is similar in spectral type to ? Pup (the only O star that clearly shows asymmetric X-ray emission-line profiles with large blueshifts), we expected to see similar emission-line characteristics. Contrary to other O star results, the emission lines of Cyg OB2 No. 8A show a large range in line centroid shifts (~-800 to +250 km s-1). However, we argue that most of the largest shifts may be unreliable and the resulting range in shifts is much less than those observed in ? Pup. Although there is one exception, the H-like Mg XII line, which shows a blueshift of -550 km s-1, there are problems associated with trying to understand the nature of this isolated large blueshifted line. To address the degree of asymmetry in these line profiles, we present Gaussian best-fit line profile model spectra from ? Pup to illustrate the expected asymmetry signature in the ?2 residuals. Comparisons of the Cyg OB2 No. 8A best-fit line profile residuals with those of ? Pup suggest that there are no indications of any statistical significant asymmetries in these line profiles. Both the line shift characteristics and lack of line asymmetries are very puzzling results. Given the very high mass-loss rate of Cyg OB2 No. 8A (approximately 5 times larger than previous Chandra-observed O supergiants), the emission lines from this star should display a significant level of line asymmetry and blueshifts as compared to other OB stars. We also discuss the implications of our results in light of the fact that Cyg OB2 No. 8A is a member of a rather tight stellar cluster, and shocks could arise at interfaces with the winds of these other stars.