  We compute the cosmological reduction of the fourth powers of the Riemann
tensor claimed to arise in string theory at order $\alpha'^{\,3}$, with overall
coefficient proportional to $\zeta(3)$, and show that it is compatible with an
$O(9,9)$ symmetry. This confirms the general result in string theory, due to
Sen, that classical string theory with $d$-dimensional translation invariance
admits an $O(d,d)$ symmetry to all orders in $\alpha'$.
