We present a conceptual design for an active neutron veto, based on boron-loaded liquid scintillator, for use in direct-detection dark matter experiments. The simulated efficiency of a 1 meter thick veto, after including the effects of neutron captures in the inner detector and inefficiencies due to feed-throughs into the veto, is greater than 99.5% for background events produced by radiogenic neutrons, while the background due to externally produced cosmogenic neutrons is reduced by more than 95%. The ability of the veto to both significantly suppress, and provide in situ measurements of, these two dominant sources of background would make the next generation of dark matter experiments much more robust, and dramatically improve the credibility of a dark matter detection claim based on the observation of a few recoil events. The veto would also allow direct extrapolation between the background-free operation of a small detector and the physics reach of a larger detector of similar construction.