An explicit construction of closed-string states is given in terms of open-string oscillators acting on the open-string Fock vacuum. The closed-open-open coupling is computed for the graviton and agrees with the standard result. The closed string states are not annihilated by the Becchi-Rouet-Stora-Tyutin operator Q. Instead they generate inner derivations which anticommute with Q. This is sufficient to insure gauge invariance of tree-level S-matrix elements. It also implies that the closed-string states obey, level by level, the linearized equation of motion of the cubic action.