  Based on archival {\it Chandra} observations with a total exposure of 1.3 Ms,
we study X-ray point sources in the Fornax cluster of galaxies, with the
primary aim of searching for intra-cluster X-ray source populations. We detect
1177 point sources out to a projected radius of $\sim$30 arcmin ($\sim$180 kpc)
from the cluster center and down to a limiting 0.5--8 keV luminosity of
$\sim3\times10^{37}{\rm~erg~s^{-1}}$. We construct source surface density
profile, after excluding sources associated with foreground stars, known
globular clusters, ultra-compact dwarfs and galactic nuclei. From this profile
we statistically identify $\sim$183 excess sources that are not associated with
the bulk stellar content of the individual member galaxies of Fornax, nor with
the cosmic X-ray background. Taking into account Poisson error and cosmic
variance, the cumulative significance of this excess is at $\gtrsim 2\,\sigma$
level (with a maximum of 3.6\,$\sigma$) outside three effective radii of the
central giant elliptical, NGC\,1399. The luminosity function of the excess
sources is found to be significantly steeper than that of the GC-hosting
sources (presumably low-mass X-ray binaries [LMXBs]), disfavoring the
possibility that unidentified GCs are primarily responsible for the excess. We
show that a large fraction of the excess can be related to the extended stellar
halo of NGC\,1399 and/or the diffuse intra-cluster light, thus providing strong
evidence for the presence of intra-cluster X-ray sources in Fornax, the second
unambiguous case for a galaxy cluster after Virgo. Other possible origins of
the excess, including supernova-kicked LMXBs and stripped nucleated dwarf
galaxies are discussed.
