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We present first results from an unbiased 50 deg^2 submillimeter Galactic survey at 250, 350, and 500 micron from the 2006 flight of the Balloon-borne Large Aperture Submillimeter Telescope (BLAST). The map has resolution ranging from 36 arcsec to 60 arcsec in the three submillimeter bands spanning the thermal emission peak of cold starless cores. We determine the temperature, luminosity, and mass of more than one thousand compact sources in a range of evolutionary stages and an unbiased statistical characterization of the population. From comparison with C^(18)O data, we find the dust opacity per gas mass, kappa r = 0.16 cm^2 g^(-1) at 250 micron, for cold clumps. We find that 2% of the mass of the molecular gas over this diverse region is in cores colder than 14 K, and that the mass function for these cold cores is consistent with a power law with index alpha = -3.22 +/- 0.14 over the mass range 14 M_sun < M < 80 M_sun. Additionally, we infer a mass-dependent cold core lifetime of t_c(M) = 4E6 (M/20 M_sun)^(-0.9) years - longer than what has been found in previous surveys of either low or high mass cores, and significantly longer than free fall or likely turbulent decay times. This implies some form of non-thermal support for cold cores during this early stage of star formation., Comment: Accepted for publication in the Astrophysical Journal. Maps available at http://blastexperiment.info/