We present the first interferometric CO(J=1->0) map of the entire H-alpha disk of M33. The 13 diameter synthesized beam corresponds to a linear resolution of 50 pc, sufficient to distinguish individual giant molecular clouds (GMCs). From these data we generated a catalog of 148 GMCs with an expectation that no more than 15 of the sources are spurious. The catalog is complete down to GMC masses of 1.5 X 10^5 M_sun and contains a total mass of 2.3 X 10^7 M_sun. Single dish observations of CO in selected fields imply that our survey detects ~50% of the CO flux, hence that the total molecular mass of M33 is 4.5 X 10^7 M_sun, approximately 2% of the HI mass. The GMCs in our catalog are confined largely to the central region (R < 4 kpc). They show a remarkable spatial and kinematic correlation with overdense HI filaments; the geometry suggests that the formation of GMCs follows that of the filaments. The GMCs exhibit a mass spectrum dN/dM ~ M^(-2.6 +/- 0.3), considerably steeper than that found in the Milky Way and in the LMC. Combined with the total mass, this steep function implies that the GMCs in M33 form with a characteristic mass of 7 X 10^4 M_sun. More than 2/3 of the GMCs have associated HII regions, implying that the GMCs have a short quiescent period. Our results suggest the rapid assembly of molecular clouds from atomic gas, with prompt onset of massive star formation.
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