By taking into account the full O(α′3) type IIB string theory corrections to the supergravity action, we compute the leading finite ’t Hooft coupling O(λ−3/2) corrections to the conductivity of strongly-coupled SU(N ) N = 4 supersymmetric Yang-Mills plasma in the large N limit. We find that the conductivity is enhanced by the corrections, in agreement with the trend expected from previous perturbative weak-coupling computations.