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 100Â ms .
The short time delay and the nearly symmetric cross-correlation function , together with the measured brightness temperature of \sim 2.5 \times 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 .