We present the first results from an ongoing survey to characterize the circumgalactic medium (CGM) of massive high-redshift galaxies detected as submillimeter galaxies (SMGs). We constructed a parent sample of 163 SMGQSO pairs with separations less than similar to 36" by cross-matching far-infrared-selected galaxies from Herschel with spectroscopically confirmed QSOs. The Herschel sources were selected to match the properties of the SMGs. We determined the sub-arcsecond positions of six Herschel sources with the Very Large Array and obtained secure redshift identification for three of those with near-infrared spectroscopy. The QSO sightlines probe transverse proper distances of 112, 157, and 198. kpc at foreground redshifts of 2.043, 2.515, and 2.184, respectively, which are comparable to the virial radius of the similar to 10(13) M circle dot halos expected to host SMGs. High-quality absorption-line spectroscopy of the QSOs reveals systematically strong H I Ly alpha absorption around all three SMGs, with rest-frame equivalent widths of similar to 2-3 A. However, none of the three absorbers exhibit compelling evidence for optically thick H I gas or metal absorption, in contrast to the dominance of strong neutral absorbers in the CGM of luminous z similar to 2 QSOs. The low covering factor of optically thick H I gas around SMGs tentatively indicates that SMGs may not have as prominent cool gas reservoirs in their halos as the coeval QSOs and that they may inhabit less massive halos than previously thought.