We use spitzer-IRAC data to identify near-infrared counterparts to submillimeter galaxies detected with Herschel-SPIRE at 250um in the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS). Using a likelihood ratio analysis we identify 146 reliable IRAC counterparts to 123 SPIRE sources out of the 159. We find that, compared to the field population, the SPIRE counterparts occupy a distinct region of 3.6 and 4.5um color-magnitude space, and we use this property to identify a further 23 counterparts to 13 SPIRE sources. The IRAC identification rate of 86% is significantly higher than those that have been demonstrated with wide-field ground-based optical and near-IR imaging of Herschel fields. We estimate a false identification rate of 3.6%, corresponding to 4 to 5 sources. Among the 73 counterparts that are undetected in SDSS, 57 have both 3.6 and 4.5um coverage. Of these 43 have [3.6] - [4.5]> 0 indicating that they are likely to be at z > 1.4. Thus, ~ 40% of identified SPIRE galaxies are likely to be high redshift (z > 1.4) sources. We discuss the statistical properties of the IRAC-identified SPIRE galaxy sample including far-IR luminosities, dust temperatures, star-formation rates, and stellar masses. The majority of our detected galaxies have 10^10 to 10^11 L_sun total IR luminosities and are not intense starbursting galaxies as those found at z ~ 2, but they have a factor of 2 to 3 above average specific star-formation rates compared to near-IR selected galaxy samples.
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