We study neutrino emission from the remnant of an inspiraling binary neutro
n star following coalescence. The mass of the merged remnant is Likely to e
xceed the stability Limit of a cold, rotating neutron star. However, the an
gular momentum of the remnant may also approach or even exceed the Kerr lim
it, J/M-2 = 1, so that total collapse may not be possible unless some angul
ar momentum is dissipated. We find that neutrino emission is very inefficie
nt in decreasing the angular momentum of these merged 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 th
e remnant may form a bar mode instability on a timescale similar to or shor
ter than the neutrino emission timescale, in which case the evolution of th
e remnant will be dominated by the emission of gravitational waves.