  We present a survey of X-ray point sources in the nearest and dynamically
young galaxy cluster, Virgo, using archival Chandra observations that sample
the vicinity of 80 early-type member galaxies. The X-ray source populations at
the outskirt of these galaxies are of particular interest. We detect a total of
1046 point sources (excluding galactic nuclei) out to a projected
galactocentric radius of $\sim$40 kpc and down to a limiting 0.5-8 keV
luminosity of $\sim$$2\times10^{38}{\rm~erg~s^{-1}}$. Based on the cumulative
spatial and flux distributions of these sources, we statistically identify
$\sim$120 excess sources that are not associated with the main stellar content
of the individual galaxies, nor with the cosmic X-ray background. This excess
is significant at a 3.5 $\sigma$ level, when Poisson error and cosmic variance
are taken into account. On the other hand, no significant excess sources are
found at the outskirt of a control sample of field galaxies, suggesting that at
least some fraction of the excess sources around the Virgo galaxies are truly
intra-cluster X-ray sources. Assisted with ground-based and HST optical imaging
of Virgo, we discuss the origins of these intra-cluster X-ray sources, in terms
of supernova-kicked low-mass X-ray binaries (LMXBs), globular clusters, LMXBs
associated with the diffuse intra-cluster light, stripped nucleated dwarf
galaxies and free-floating massive black holes.
