It is an open question whether and how gravitational wave events involving neutron stars can be preceded by electromagnetic counterparts. This Letter shows that the collision of two neutron stars with magnetic fields well below magnetar-level strengths can produce millisecond fast-radio-burst-like transients. Using global force-free electrodynamics simulations, we identify the coherent emission mechanism that might operate in the common magnetosphere of a binary neutron star system prior to merger. We predict that the emission show have frequencies in the range of 10-20 GHz for magnetic fields of B^{*}=10^{11} G at the surfaces of the stars.