  We present the discovery of optical/X-ray flux correlations on rapid
timescales in the low/hard state of the Galactic black hole GX 339-4. The
source had recently emerged from outburst and was associated with a
relatively-faint counterpart with mag V~17. The optical (VLT/ULTRACAM) and
X-ray (RXTE/PCA) data show a clear positive cross-correlation function (CCF)
signal, with the optical peak lagging X-rays by ~ 150 ms, preceded by a shallow
rise and followed by a steep decline along with broad anti-correlation dips.
Examination of the light curves shows that the main CCF features are reproduced
in superpositions of flares and dips. The CCF peak is narrow and the X-ray
auto-correlation function (ACF) is broader than the optical ACF, arguing
against reprocessing as the origin for the rapid optical emission. X-ray
flaring is associated with spectral hardening, but no corresponding changes are
detected around optical peaks and dips. The variability may be explained in the
context of synchrotron emission with interaction between a jet and a corona.
The complex CCF structure in GX 339-4 has similarities to that of another
remarkable X-ray binary XTE J1118+480, in spite of showing a weaker maximum
strength. Such simultaneous multi-wavelength, rapid timing studies provide key
constraints for modeling the inner regions of accreting stellar sources.
