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 ) _ { \infty } = 0.14 ) and high compaction ( ( m / R ) _ { \infty } = 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 ) _ { \infty } = 0.14 ( ( m / R ) _ { \infty } = 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 .