  We compare the rotation rate of neutron stars in low-mass X-ray binaries
(LMXBs) with the orbital period of the binaries. We find that, while short
orbital period LMXBs span a range of neutron star rotation rates, all the long
period LMXBs have fast rotators. We also find that the rotation rates are
highest for the systems with the highest mean mass accretion rates, as can be
expected if the accretion rate correlates with the orbital period. We show that
these properties can be understood by a balance between spin-up due to
accretion and spin-down due to gravitational radiation. Our scenario indicates
that the gravitational radiation emitted by these systems may be detectable by
future ground-based gravitational wave detectors.
