  We present the discovery of fast infrared/X-ray correlated variability in the
black-hole transient GX 339-4. The source was observed with sub-second time
resolution simultaneously with VLT/ISAAC and RXTE/PCA in August 2008, during
its persistent low-flux highly variable hard state. The data show a strong
correlated variability, with the infrared emission lagging the X-ray emission
by 100 ms. The short time delay and the nearly symmetric cross-correlation
function, together with the measured brightness temperature of ~2.5 x 10^6 K,
indicate that the bright and highly variable infrared emission most likely
comes from a jet near the black hole. Under standard assumptions about jet
physics, the measured time delay can provide us a lower limit of Gamma > 2 for
the Lorentz factor of the jet. This suggests that jets from stellar-mass black
holes are at least mildly relativistic near their launching region. We discuss
implications for future applications of this technique.
