We present the results of a long-term study of the black hole candidate GX 339−4 using simultaneous radio (from the Australia Telescope Compact Array) and X-ray (from the Rossi X-ray Timing Explorer and BeppoSAX) observations performed between 1997 and 2000. We find strong evidence for a correlation between these two emission regimes that extends over more than three decades in X-ray flux, down to the quiescence level of GX 339−4. This is the strongest evidence to date for such strong coupling between radio and X-ray emission. We discuss these results in light of a jet model that can explain the radio/X-ray correlation. This could indicate that a significant fraction of the X-ray flux that is observed in the low-hard state of black hole candidates may be due to optically thin synchrotron emission from the compact jet.