We present the discovery of an exciting optical/X-ray flux correlation on rapid timescales of tens of milli-seconds in the low/hard state of the Galactic black hole GX 339-4. The optical (VLT) and X-ray (RXTE) data show a clear positive cross-correlation function (CCF) signal, with optical lagging X-rays by ~150 ms, preceded by a shallow rise and followed by a steep decline with anti-correlation dips. Both optical and X-ray power density spectra are qualitatively similar with a break or QPO-like feature at timescales of ~20 s. The CCF is narrow and the X-ray auto-correlation function (ACF) is broader than the optical ACF, arguing against reprocessing as the emission mechanism for the optical power. We discuss the observations in terms of a cyclotron radiation model formulated 26 years ago by Andy Fabian, as well as an alternative jet synchrotron model. The complex CCF structure suggests similarities to another remarkable X-ray binary XTE J1118+480. Such rapid timing studies are opening up new parameter space for accretion studies in stellar sources.