  General relativity predicts that a rotating body produces a frame-dragging
(or Lense-Thirring) effect: the orbital plane of a test particle in a
non-equatorial orbit precesses about the body's symmetry axis. In this paper we
compute the precession frequencies of circular orbits around rapidly rotating
neutron stars for a variety of masses and equations of state. The precession
frequencies computed are expressed as numerical functions of the orbital
frequency observed at infinity. The post-Newtonian expansion of the exact
precession formula is examined to identify the relative magnitudes of the
precession caused by the Lense-Thirring effect, the usual Newtonian quadrupole
effect and relativistic corrections. The first post-Newtonian correction to the
Newtonian quadrupole precession is derived in the limit of slow rotation. We
show that the post-Newtonian precession formula is a good approximation to the
exact precession close to the neutron star in the slow rotation limit (up to
\sim 400 Hz in the present context).
  The results are applied to recent RXTE observations of neutron star low-mass
X-ray binaries, which display kHz quasi-periodic oscillations and, within the
framework of beat frequency models, allow the measurement of both the neutron
star spin frequency and the Keplerian frequency of the innermost ring of matter
in the accretion disk around it. For a wide range of realistic equations of
state, we find that the predicted precession frequency of this ring is close to
one half of the low-frequency (\sim 20 - 35 Hz) quasi-periodic oscillations
seen in several Atoll sources.
