  We determine the innermost stable circular orbit (ISCO) of binary neutron
stars (BNSs) by performing dynamical simulations in full general relativity.
Evolving quasiequilibrium (QE) binaries that begin at different separations, we
bracket the location of the ISCO by distinguishing stable circular orbits from
unstable plunges. We study Gamma=2 polytropes of varying compactions in both
corotational and irrotational equal-mass binaries. For corotatonal binaries we
find an ISCO orbital angular frequency somewhat smaller than that determined by
applying turning-point methods to QE initial data. For the irrotational
binaries the initial data sequences terminate before reaching a turning point,
but we find that the ISCO frequency is reached prior to the termination point.
Our findings suggest that the ISCO frequency varies with compaction but does
not depend strongly on the stellar spin. Since the observed gravitational wave
signal undergoes a transition from a nearly periodic ``chirp'' to a burst at
roughly twice the ISCO frequency, the measurement of its value by laser
interferometers (e.g LIGO) will be important for determining some of the
physical properites of the underlying stars
