We present high S/N, high-resolution observations of the Ca II absorption toward 3C 273 and SN 1991T in a sensitive metal-line probe of the interstellar and intergalactic gas out to the Virgo Cluster over pathlengths separated by only 1.4 on the sky. In addition to marked differences in the low-velocity gas, we detect weak Ca II components at upsilon-LSR = -87, +215, and +263 km s-1 toward SN 1991T that are absent in the 3C 273 spectrum. Given the velocity (upsilon-LSR = 1733 km s-1) of the SN 1991T host galaxy (NGC 4527), we ascribe these features to the Galactic high-velocity cloud (HVC) phenomenon primarily observed in H I 21 cm emission. Although the metal-line counterparts to HVCs have been rarely observed, our ability to detect these weak Ca II components is beyond the sensitivity of almost all previous absorption-line work on extragalactic sources outside the vicinity of the Magellanic Clouds. We discuss the possibility that metal-absorbing HVCs of low column density could be common throughout the Galactic halo and the resulting implications for the halo interpretation of multicomponent QSO absorption-line systems.