  The X-ray source 4U1820-30 in the globular cluster NGC 6624 is known as the
most compact binary among the identified X-ray binaries. Having an orbital
period of 685.0 s, the source consists of a neutron star primary and likely
0.06--0.08 Msun white dwarf secondary. Here we report on far-ultraviolet (FUV)
observations of this X-ray binary, made with the Space Telescope Imaging
Spectrograph on board the Hubble Space Telescope. From our Fourier spectral
analysis of the FUV timing data, we obtain a period of 693.5+/-1.3 s, which is
significantly different from the orbital period. The light curve folded at this
period can be described by a sinusoid, with a fractional semiamplitude of 6.3%
and the phase zero (maximum of the sinusoid) at MJD 50886.015384+/-0.000043
(TDB). While the discovered FUV period may be consistent with a hierarchical
triple system model that was previously considered for 4U 1820-30, we suggest
that it could instead be the indication of superhump modulation, which arises
from an eccentric accretion disk in the binary. The X-ray and FUV periods would
be the orbital and superhump periods, respectively, indicating a 1% superhump
excess and a white-dwarf/neutron-star mass ratio around 0.06. Considering 4U
1820-30 as a superhump source, we discuss the implications.
