We report on a rapid fading of GX 339-4 to its lowest ever observed X-ray flux level. In response to the recent report of the start of an outburst of GX 339-4 (ATel #4162), we submitted a Swift TOO to check its X-ray flux. The observations were performed on July 8, 2012, from 14:00:59 to 15:53:55 UT. The live on-source exposure time of the observations was 2193 seconds. To our surprise, the source was not significantly detected, with a count rate of 0.0025+-0.0017 cts/sec from 0.3-10 keV, using Phil Evans' standard pipeline (Evans et al.