We present the first detailed dissection of the circumgalactic medium (CGM) of massive starburst galaxies at z > 2. Our target is a submillimeter galaxy (SMG) at z = 2.674 that has a star formation rate of 1200 $M_odot$/yr and a molecular gas reservoir of $1.3times10^{11} M_odot$. We characterize its CGM with two background QSOs at impact parameters of 93 kpc and 176 kpc. We detect strong HI and metal-line absorption near the redshift of the SMG towards both QSOs, each consisting of three main subsystems spanning over 1500 km/s. The absorbers show remarkable kinematic and metallicity coherence across a separation of 86 kpc. In particular, the cool gas in the CGM of the SMG exhibits high HI column densities ($log N_{rm HI}/{rm cm}^{-2} = 20.2, 18.6$), low metallicities ([M/H] $approx$ -2.0), and similar radial velocities ($approx$ -300 km/s). While the HI column densities match previous results on the CGM around QSOs at z > 2, the metallicities are lower by more than an order of magnitude, making it an outlier in the line width$-$metallicity relation of damped Ly$alpha$ absorbers. The large physical extent, the velocity coherence, the high surface density, and the low metallicity are all consistent with the cool, inflowing, and near-pristine gas streams predicted to penetrate hot massive halos at z > 1.5. We estimate a total gas accretion rate of ~100 $M_odot$/yr from three such streams, which falls short of the star formation rate but is consistent with simulations. At this rate, it takes about a gigayear to acquire the molecular gas reservoir of the central starburst.
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