We report the first detection of a submillimeter galaxy (SMG) in CO(1 →0) emission using the GBT. We identify a line with Δv_(FWHM) ~1000 kms^(−1) in the 1 cm spectrum of SMM J13120+4242 at z = 3.408, which is significantly greater than the width of the previously detected CO(4→3) line. If the observed CO(1→0) line profile arises from a single object and not several merging objects, the CO(4 →3)/CO(1→0) brightness temperature ratio of ~0.26 suggests n(H_2) > 10^3 cm^(−3) and the presence of sub-thermally excited gas. The 10σ integrated line flux implies a cold molecular gas mass M(H2) ~10^(11)M_⊙, comparable to the dynamical mass estimate and four times larger than the H_2 mass found from the CO(4 →3) line. While our observations confirm that this SMG is massive and highly gas-rich, they also suggest that J_(upper) > 3 transitions of CO may not accurately trace cold, diffuse molecular gas in SMGs.