We have obtained three epochs of Chandra ACIS-I observations (totaling ~184 ks) of the nearby spiral galaxy NGC 300 to study the logN-logS distributions of its X-ray point-source population down to ~2 × 10-15 erg s-1 cm-2 in the 0.35-8 keV band (equivalent to ~1036 erg s-1). The individual epoch logN-logS distributions are best described as the sum of a background active galactic nucleus (AGN) component, a simple power law, and a broken power law, with the shape of the logN-logS distributions sometimes varying between observations. The simple power law and AGN components produce a good fit for "persistent" sources (i.e., with fluxes that remain constant within a factor of ~2). The differential power-law index of ~1.2 and high fluxes suggest that the persistent sources intrinsic to NGC 300 are dominated by Roche-lobe-overflowing low-mass X-ray binaries. The variable X-ray sources are described by a broken power law, with a faint-end power-law index of ~1.7, a bright-end index of ~2.8-4.9, and a break flux of ~ 8× {10}-15 erg s-1 cm-2 (~4 × 1036 erg s-1), suggesting that they are mostly outbursting, wind-fed high-mass X-ray binaries, although the logN-logS distribution of variable sources likely also contains low-mass X-ray binaries. We generate model logN-logS distributions for synthetic X-ray binaries and constrain the distribution of maximum X-ray fluxes attained during outburst. Our observations suggest that the majority of outbursting X-ray binaries occur at sub-Eddington luminosities, where mass transfer likely occurs through direct wind accretion at ~1%-3% of the Eddington rate.
