In a study of Chandra High Energy Transmission Grating spectra of Algol, we clearly detect Doppler shifts caused by the orbital motion of Algol B. These data provide the first definitive proof that the X-ray emission of Algol is dominated by the secondary, in concordance with expectations that the primary B8 component should be X-ray-dark. However, the measured Doppler shifts are slightly smaller than might be expected, implying an effective orbital semimajor axis of about 10 Rsolar instead of 11.5 Rsolar for the Algol B center of mass. This could be caused by a small contribution of Algol A, possibly through accretion, to the observed X-ray flux, in which case such a contribution does not exceed 10%-15%. We suggest that the more likely explanation is an asymmetric corona biased toward the system center of mass by the tidal distortion of the surface of Algol B. A detailed analysis of the profiles of the strongest lines indicates the presence of excess line broadening amounting to approximately 150 km s-1 above that expected from thermal motion and surface rotation. Possible explanations for this additional broadening include turbulence, flows or explosive events, or rotational broadening from a radially extended corona. We favor the latter scenario and infer that a significant component of the corona at temperatures less than 107 K has a scale height of order the stellar radius. This interpretation is supported by the shape of the X-ray light curve and tentative detection of a shallow dip at secondary eclipse. We also examine the O VII intercombination and forbidden lines in a Low Energy Transmission Grating Spectrograph observation and find no change in their relative line fluxes as the system goes from quadrature to primary eclipse. Since these lines appear to be strongly affected by UV irradiation from Algol A through radiative excitation of the 23S-->23P transition, this supports the conjecture that the corona of Algol B at temperatures of several million kelvins must be significantly extended and/or located toward the poles to avoid being shadowed from Algol A during primary eclipse.