We report on the Chandra observations of the elliptical galaxy NGC 1399, co
ncentrating on the X-ray sources identified with globular clusters (GCs). A
large fraction of the 2-10 keV X-ray emission in the 8' x 8' Chandra image
is resolved into point sources with luminosities greater than or equal to5
x 10(37) ergs s(-1). These sources are most likely low-mass X-ray binaries
(LMXBs). In a region imaged by the Hubble Space Telescope, about 70% of th
e X-ray sources are located within GCs. This association suggests that in g
iant elliptical galaxies luminous X-ray binaries preferentially form in GCs
. Many of the GC sources have super-Eddington luminosities (for an accretin
g neutron star), and their average luminosity is higher than the non-GC sou
rces. The X-ray spectral properties of both GC and non-GC sources are simil
ar to those of LMXBs in our Galaxy. Two of the brightest sources, one of wh
ich is in a GC, have an ultrasoft spectrum, similar to that seen in the hig
h state of black hole candidates. The "apparent" super-Eddington luminosity
in many cases may be due to multiple LMXB systems within individual GCs bu
t with some of the most extremely luminous systems containing massive black
holes.