We present the first low-luminosity [LX (5-10) × 1036 ergs 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 ellipses 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 × 1037 ergs s-1 that was recently suggested as being a general feature of LMXB XLFs. In NGC 3379, on the other hand, we find a localized excess over the power-law XLF at ~4 × 1037 ergs s-1, but with a marginal significance of ~1.6 σ. Because of the small number of luminous sources, we cannot constrain the high-luminosity break (at 5 × 1038 ergs s-1) found in a large sample of early-type galaxies. For our two galaxies, the ratios of the integrated LMXB X-ray luminosities to the optical luminosities differ by a factor of 4, but are consistent with the general trend of a positive correlation between the X-ray-to-optical luminosity ratio and the globular cluster specific frequency.
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