One hundred and seven ultraluminous X-ray sources (ULXs) with 0.3-10.0 keV luminosities in excess of 10³⁹ erg s^-1 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 Catalogue and the Infrared Astronomical Satellite survey. The galaxy sample spans all Hubble types, a four-decade range in mass, 7.5 < log (M/M_sun) < 11.4, and in star formation rate, 0.0002 < SFR(M_sun yr^-1) <= 3.6. ULXs are detected in this sample at rates of one per 3.2 x 10¹⁰ M_sun, one per ~0.5 M_sun yr^-1 star formation rate, and one per 57 Mpc³ corresponding to a luminosity density of ~2 x 10³⁷ erg s^-1 Mpc^-3. At these rates, the authors estimate as many as 19 additional ULXs remain undetected in fainter dwarf galaxies within the survey volume. An estimated 14 objects, or 13%, of the 107 ULX candidates are expected to be background sources. The differential ULX luminosity function shows a power-law slope alpha ~ -0.8 to -2.0 with an exponential cutoff at ~20 x 10³⁹ erg s^-1 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_X ~ 10⁴¹ erg s^-1, 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 2 x 10⁴¹ erg s^-1, requiring a new population class to explain these extreme objects. This table was created by the HEASARC in November 2011 based on an electronic version of Table 1 from the reference paper that was obtained from the ApJ web site. This is a service provided by NASA HEASARC .