We present a rapid timing analysis of VLT (optical) and RXTE data of the Galactic black hole GX 339-4 in the low/hard state in June 2007, soon after emerging from outburst. Both optical and X-ray power density spectra are qualitatively similar with QPO-like feature or a break around 0.05-0.1 Hz. A cross-correlation function (CCF) analysis finds no positive correlation on timescales on 1 s or longer, similar to previous observations in the bright state. Searching for signal on the fastest (50 ms) timescales available, on the other hand, a significant cross-correlation peak is detected, with the optical lagging the X-rays by 150 ms. The CCF is narrow with a shallow rise and sharp decline to an anti-correlation dip. The X-ray auto-correlation function (ACF) is broader than the optical ACF, arguing against re-processing as the emission mechanism for the optical power. Similarities and differences with respect to the complex behaviour of XTE J1118+480 are discussed and the need for further rapid variability observations of this fascinating source are emphasized.