The high-frequency peaked BL Lac PKS 2155-304 at redshift z=0.116 is a well-known VHE (>100 GeV) gamma-ray emitter. Since 2002 its VHE flux has been monitored using the H.E.S.S. stereoscopic array of imaging atmospheric-Cherenkov telescopes in Namibia. During the July 2006 dark period, the average VHE flux was measured to be more than ten times typical values observed from the object. This article focuses solely on an extreme gamma-ray outburst detected in the early hours of July 28, 2006 (MJD 53944). The average flux observed during this outburst is I(>200 GeV) = (1.72$pm$$0.05_{rm stat}$$pm$$0.34_{rm syst}$) $times$ 10$^{-9}$ cm$^{-2}$ s$^{-1}$, corresponding to ~7 times the flux, I(>200 GeV), observed from the Crab Nebula. Peak fluxes are measured with one-minute time scale resolution at more than twice this average value. Variability is seen up to ~600 s in the Fourier power spectrum, and well-resolved bursts varying on time scales of ~200 seconds are observed. There are no strong indications for spectral variability within the data. Assuming the emission region has a size comparable to the Schwarzschild radius of a ~10$^9 M_odot$ black hole, Doppler factors greater than 100 are required to accommodate the observed variability time scales.
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