  We present the first low luminosity (LX > 5 - 10 1036 erg s-1) X-ray
luminosity functions (XLFs) of low-mass X-ray binaries (LMXBs) determined for
two typical old elliptical galaxies, NGC 3379 and NGC 4278. Because both
galaxies contain little diffuse emission from hot ISM and no recent significant
star formation (hence no high-mass X-ray binary contamination), they provide
two of the best homogeneous sample of LMXBs. With 110 and 140 ks Chandra ACIS
S3 exposures, we detect 59 and 112 LMXBs within the D25 ellipse of NGC 3379 and
NGC 4278, respectively. The resulting XLFs are well represented by a single
power-law with a slope (in a differential form) of 1.9 0.1. In NGC 4278, we can
exclude the break at LX ~ 5 x 1037 erg s-1 that was recently suggested to be a
general feature of LMXB XLFs. In NGC 3379 instead we find a localized excess
over the power law XLF at ~4 x 1037 erg s-1, but with a marginal significance
of ~1.6s. Because of the small number of luminous sources, we cannot constrain
the high luminosity break (at 5 x 1038 erg s-1) found in a large sample of
early type galaxies. While the optical luminosities of the two galaxies are
similar, their integrated LMXB X-ray luminosities differ by a factor of 4,
consistent with the relation between the X-ray to optical luminosity ratio and
the globular cluster specific frequency.
