The average prompt-fission-neutron multiplicity $bar{ u}$ is of significance in the areas of nuclear theory, nuclear nonproliferation, and nuclear energy. In this work, the surrogate-reaction method has been used for the first time to indirectly determine $bar{ u}$ for $^{239}$Pu($n$,$f$) via $^{240}$Pu($alpha$,$alpha^{prime}f$) reactions. A $^{240}$Pu target was bombarded with a beam of 53.9-MeV $alpha$ particles. Scattered $alpha$ particles, fission products, and neutrons were measured with the NeutronSTARS detector array. Values of $bar{ u}$ were obtained for a continuous range of equivalent incident neutron energies between 0.25--26.25~MeV, and the results agree well with direct neutron measurements.
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