We show that closed strings can be incorporated into a bosonic open-string theory by a suitable enlargement of the open-string Fock space. We present an explicit construction of the states in this space in terms of open-string oscillators. The couplings between closed- and open-string states are those deduced from factorization over the closed-string poles of the nonplanar one-loop open-string diagram. We also construct a field theory of closed strings starting from Witten's field theory of open bosonic strings. We show that the interaction vertex is Becchi-Rouet-Stora-Tyutin invariant and that associativity anomalies are absent. We also calculate the residues of poles in the four-tachyon tree amplitude, finding agreement with dual theory.