  It has been suggested that the 170 day period in the light curve of the low
mass X-ray binary 4U 1820-30 arises from the presence of a third body with a
large inclination to the binary orbit. We show that this long period motion
arises if the system is librating around the stable fixed point in a Kozai
resonance. We demonstrate that mass transfer drives the system toward this
fixed point, and calculate, both analytically and via numerical integrations,
that the period of libration is of order 170 days when the mutual inclination
is near the Kozai critical value. The non-zero eccentricity of the binary,
combined with tidal dissipation, implies that the rate of change of the binary
period would be slower than, or even of opposite sign to, that implied by
standard mass transfer models. If the 170 day period results from libration,
then, contrary to appearances, the orbital period of the inner binary is
increasing with time; in that case, (e/0.009)^2Q/k_2 > 2.5 x 10^9, where k_2 =
0.01 is the tidal Love number and e = 0.009 is the fiducial eccentricity of the
inner binary. It appears unlikely that the observed negative period derivative
results from the smaller than expected (but positive) value of \dot P combined
with the previously suggested acceleration of the system in the gravitational
field of the host globular cluster NGC 6624. The discrepancy between the
observed and expected period derivative requires further investigation.
