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 ⊙ yr −1 and a molecular gas reservoir of 1.3 × 10 11 M ⊙ . We characterize its CGM with two background QSOs at impact parameters of 93 kpc and 176 kpc. We detect strong H I and metal-line absorption near the redshift of the SMG towards both QSOs, each consisting of three main subsystems spanning over 1500 km s −1 . 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 H I column densities (log N HI /cm −2 = 20.2, 18.6), low metallicities ([M/H] ≈ −2.0), and similar radial velocities (δv ∼ −300 km s −1 ). While the H I column densities match previous results on the CGM around QSOs at z > 2, the metallicities are lower by more than an order-ofmagnitude. 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 ⊙ yr −1 from three such streams, which falls short of the star formation rate but is consistent with simulations. At this rate, it takes about a billion years to acquire the molecular gas reservoir of the central starburst.