  The black-hole binary LMC X-3 is known to be variable on time scales of days
to years. We investigate X-ray and ultraviolet variability in the system as a
function of the 1.7 day binary phase using a 6.4 day observation with the Rossi
X-ray Timing Explorer (RXTE) from December 1998. An abrupt 14% flux decrease,
lasting nearly an entire orbit, is followed by a return to previous flux
levels. This behavior occurs twice, at nearly the same binary phase, but it is
not present in consecutive orbits. When the X-ray flux is at lower intensity, a
periodic amplitude modulation of 7% is evident in data folded modulo the
orbital period. The higher intensity data show weaker correlation with phase.
This is the first report of X-ray variability at the orbital period of LMC X-3.
Archival RXTE observations of LMC X--3 during a high flux state in December
1996 show similar phase dependence. An ultraviolet light curve obtained with
the High Speed Photometer aboard the Hubble Space Telescope shows orbital
modulation consistent with that in the optical, caused by the ellipsoidal
variation of the spatially deformed companion.
  The X-ray spectrum of LMC X-3 can be acceptably represented by a
phenomenological disk-black-body plus a power law. Changes in the spectrum of
LMC X-3 during our observations are compatible with earlier observations during
which variations in the 2-10 keV flux are tracked closely by the disk geometry
spectral model parameter.
