  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 (1998), and show that, when compared
to the Hubble Deep Field North and South, the Virgo Cluster contains an excess
of objects with magnitudes I > 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 = 27.31
+0.27/-0.17 and that the cluster contains a small, but significant, excess of
stars that are up to ~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 < [Fe/H] <-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) cannot 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.
