We study neutrino emission from the remnant of an inspiraling binary neutron star following coalescence. The mass of the merged remnant is likely to exceed the stability limit of a cold, rotating neutron star. However, the angular momentum of the remnant may also approach or even exceed the Kerr limit, J/M^2 = 1, so that total collapse may not be possible unless some angular momentum is dissipated. We find that neutrino emission is very inefficient in decreasing the angular momentum of these

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... ged objects and may even lead to a small increase in J/M^2. We illustrate these findings with a post-Newtonian, ellipsoidal model calculation. Simple arguments suggest that the remnant may form a bar mode instability on a timescale similar to or shorter than the neutrino emission timescale, in which case the evolution of the remnant will be dominated by the emission of gravitational waves.