We have used the WFPC2 camera of the Hubble Space Telescope to obtain deep F814W images of a blank field in the Virgo Cluster located 41 \arcmin northwest of M87 . We perform star counts in that field , and in another Virgo field observed by Ferguson , Tanvir , & von Hippel ( 30 ) , and show that , when compared to the Hubble Deep Field North and South , the Virgo Cluster contains an excess of objects with magnitudes I \gtrsim 27 . We attribute this excess to a population of intracluster red-giant branch ( IC-RGB ) stars . By modeling the luminosity function of these stars , we show that the tip of the Virgo RGB is at I _ { TRGB } \sim 27.31 ^ { +0.27 } _ { -0.17 } and that the cluster contains a small , but significant , excess of stars that are up to \sim 1 mag brighter than this tip . If this luminous component is due entirely to stars on the asymptotic giant branch ( AGB ) , it implies an age for the population of > 2 Gyr ; if foreground RGB stars contribute to the luminous tail , then the derived age for the stars is older still . The luminosity function also suggests that most of the intracluster stars are moderately metal-rich ( -0.8 \lesssim [ Fe/H ] \lesssim - 0.2 ) , a result consistent with that expected from stars that have been tidally stripped from intermediate luminosity galaxies . Additionally , a comparison with the planetary nebulae in our field also supports this view , although the existence of a more metal-poor population ( from stripped dwarfs ) can not be ruled out . Our derived average surface brightness , \mu _ { I } = 27.9 ^ { +0.3 } _ { -0.5 } mag arcsec ^ { -2 } for Virgo ’ s diffuse component suggests that intracluster stars contribute 10 % to 20 % of the cluster ’ s total I -band luminosity .