Observations of the black hole X-ray binary V404 Cyg with the very long baseline interferometer HSA (the High Sensitivity Array) have detected the source at a frequency of 8.4 GHz, providing a source position accurate to 0.3 mas relative to the calibrator source. The observations put an upper limit of 1.3 mas on the source size (5.2 AU at 4 kpc) and a lower limit of 7 x 10^6 K on its brightness temperature during the normal quiescent state, implying that the radio emission must be non-thermal, most probably synchrotron radiation, possibly from a jet. The radio lightcurves show a short flare, with a rise time of about 30 min, confirming that the source remains active in the quiescent state.