We compute the cosmological reduction of the fourth powers of the Riemann tensor claimed to arise in string theory at order α^{'}^{3}, with an overall coefficient proportional to ζ(3), and show that it is compatible with an O(9,9) symmetry. This confirms the general result in string theory, due to Sen [O(d)×O(d) symmetry of the space of cosmological solutions in string theory, scale factor duality and two-dimensional black holes, Phys. Lett. B 271, 295 (1991)PYLBAJ0370-269310.1016/0370-2693(91)90090-D], that classical string theory with d-dimensional translation invariance admits an O(d,d) symmetry to all orders in α^{'}.