One hundred seven ultraluminous X-ray (ULX) sources with 0.3-10.0 keV luminosities in excess of 1e39 erg/s are identified in a complete sample of 127 nearby galaxies. The sample includes all galaxies within 14.5 Mpc above the completeness limits of both the Uppsala Galaxy Catalog and the Infrared Astronomical Satellite survey. The galaxy sample spans all Hubble types, a four decade range in mass and in star-formation rate. ULXs are detected in this sample at rates of one per 3.2e10 solar mass, one per 0.5 solar mass/year star-formation rate, and one per 57 cubic Mpc corresponding to a luminosity density of ~2e37 erg/s/Mpc3. At these rates we estimate as many as 19 additional ULXs remain undetected in fainter dwarf galaxies within the survey volume. An estimated 14 or 13%, of the 107 ULX candidates are expected to be background sources. The differential ULX luminosity function shows a power law slope of -1.2 to -2.0 with an exponential cutoff at 2e40 erg/s with precise values depending on the model and on whether the ULX luminosities are estimated from their observed numbers of counts or, for a subset of candidates, from their spectral shapes. Extrapolating the observed luminosity function predicts at most one very luminous ULX, L~1e41 erg/s, within a distance as small as 100 Mpc. The luminosity distribution of ULXs within the local universe cannot account for the recent claims of luminosities in excess of 2e41 erg/s requiring a new population class to explain these extreme objects.
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