Chandra X-ray imaging spectroscopy of the nearby Herbig Ae star HD 163296 at 100 AU angular resolution is reported. A point-like, soft (kT~0.5 keV), emission-line source is detected at the location of the star with an X-ray luminosity of 4.0e29 erg/s. In addition, faint emission along the direction of a previously-detected Ly-alpha-emitting jet and Herbig-Haro outflow may be present. The relatively low luminosity, lack of a hard spectral component, and absence of strong X-ray variability in HD 163296 can be explained as originating from optically-thin shock-heated gas accreting onto the stellar surface along magnetic field lines. This would require a (dipole) magnetic field strength at the surface of HD 163296 of at least ~100 G and perhaps as high as several kG. HD 163296 joins the T Tauri star TW Hya in being the only examples known to date of pre-main-sequence stars whose quiescent X-ray emission appears to be completely dominated by accretion.