This paper considers play in a two-person zero-sum differential game where the dynamics are given by a differential equation with additive white noise. Feedback strategies are employed. Standard results from control theory show that the maximizing player has an optimal response to any pre-announced strategy of the minimizing player. Here it is shown that the minimizing player can achieve the upper value of the game by playing a strategy which is constructed by performing a pointwise min-max on a certain fixed Hamiltonian function.