Nineteen fields have been observed in the nearby spiral galaxy M33 with the Owens Valley Millimeter-Wave Interferometer at 7″-8″ (30 pc) resolution detecting a total of 38 individual molecular clouds. The velocity widths, diameters, peak brightness temperatures, and masses of the clouds are very similar to those of Galactic giant molecular clouds (GMCs). The velocity widths and diameters of the M33 clouds are related by VFWHM = (1.2-0.6+1.3)Dpc0.5±0.2. which agrees within the errors with the velocity-diameter relation obtained for Galactic GMCs. The masses derived from the virial theorem and those derived from the integrated CO line fluxes agree to within 10% in the mean for this sample, implying that in this region of M33 the value of the conversion factor from CO flux to H2 column density, α, is similar to that of our own Galaxy. This is the first direct confirmation that the Galactic value of α is appropriate in an external galaxy. The clouds within 200 pc of the nucleus have elevated CO brightness temperatures, possibly due to an increased ultraviolet radiation field. The mass spectrum of clouds is consistent with that derived in the Galaxy for M = (0.8-4) × 105 M⊙ but shows a total lack of clouds with masses greater than 4 × 105 M⊙. Comparison of the flux detected with the interferometer with single-dish data indicates that roughly 50% of the molecular gas resides in structures less massive than 0.8 × 105 M⊙, in contrast to the Galaxy, where only 15% of the H2 mass is in these smaller structures. A simple model is proposed to explain the high-mass cutoff as arising from the competing processes of cloud growth through accretion and cloud destruction due to star formation.