A fine analysis of spectral line widths and Doppler shifts employing Fourier transform and cross-correlation techniques has been applied to Chandra HETG spectra obtained in 1999 October of the rapidly rotating young star AB Doradus in order to investigate its coronal topology. The observation lasted 52.3 ks, covering 1.2 rotation periods. The X-ray light curve obtained from integrating the dispersed signal revealed a moderate intensity flare midway through the exposure in which the count rate increased sharply by about 50% and subsequently decayed over the next 10 ks. We find no significant Doppler shifts in the spectra or modulation of the light curve that could be attributed to rotation of dominant coronal structures at this epoch. Individual spectral line widths are statistically consistent with thermal broadening and formally require no rotational broadening, while the 1σ limit to rotational broadening corresponds to a compact corona restricted to latitudes <57°. Fourier analysis suggests a small amount of rotational broadening is present consistent with a corona restricted largely to the poles, and excludes models with surface rotational broadening or greater. These results present direct spectroscopic evidence that the dominant coronal activity on rapidly rotating active stars is associated with the dark polar spots commonly seen in photospheric Doppler images and support models in which these spots are of mixed magnetic polarity that forms closed loops.