  We introduce a new numerical scheme for solving the initial value problem for
quasiequilibrium binary neutron stars allowing for arbitrary spins. The coupled
Einstein field equations and equations of relativistic hydrodynamics are solved
in the Wilson-Mathews conformal thin sandwich formalism. We construct sequences
of circular-orbit binaries of varying separation, keeping the rest mass and
circulation constant along each sequence. Solutions are presented for
configurations obeying an n=1 polytropic equation of state and spinning
parallel and antiparallel to the orbital angular momentum. We treat stars with
moderate compaction ((m/R) = 0.14) and high compaction ((m/R) = 0.19). For all
but the highest circulation sequences, the spins of the neutron stars increase
as the binary separation decreases. Our zero-circulation cases approximate
irrotational sequences, for which the spin angular frequencies of the stars
increases by 13% (11%) of the orbital frequency for (m/R) = 0.14 ((m/R) = 0.19)
by the time the innermost circular orbit is reached. In addition to leaving an
imprint on the inspiral gravitational waveform, this spin effect is measurable
in the electromagnetic signal if one of the stars is a pulsar visible from
Earth.
