  We present outburst spectroscopy of GX339-4 which may reveal the motion of
its elusive companion star. NIII lines exhibit sharp emission components moving
over ~300 km/s in a single night. The most plausible interpretation of these
components is that they are formed by irradiation of the companion star and the
velocities indicate its orbital motion. We also detect motion of the wings of
the HeII 4686A line and changes in its morphology. No previously proposed
period is consistent with periodic behavior of all of these measures. However,
consistent and sensible solutions are obtained for periods around 1.7 days. For
the best period, 1.7557 days, we estimate a mass function of 5.8 +/- 0.5 Msun.
Even allowing for aliases, the 95% confidence lower-limit on the mass function
is 2.0 Msun. GX339-4 can therefore be added to the list of dynamical black hole
candidates. This is supported by the small motion in the wings of the HeII
line; if the compact object velocity is not larger than the observed motion
then the mass ratio is q < 0.08, similar to other systems harboring black
holes. Finally, we note that the sharp components are not always present, but
do seem to occur within a repeating phase range. This appears to migrate
between our epochs of observation, and may indicate shielding of the companion
star by a variable accretion geometry such as a warp.
