An exceptional -ray outburst from 3C 279 is detected by {\it Fermi}-Large Area Telescope (LAT) in 2015 June. In the energy range of 0.1300 GeV, the highest flux measured is (39.12.5) 10 \phflux, which is the highest -ray flux ever detected from 3C 279, exceeding the previous historically brightest flare observed by {\it EGRET} in 1996. The high activity period consists of three major flares with the last one being the brightest. All but one flares show a faster rise and slower decay pattern and at the peak of the activity, the -ray spectrum is found to show a clear signature of break/curvature. The obtained spectral parameters hint for the peak of the inverse Compton emission to lie in the LAT energy range (around 1 GeV) which is in contrast to that seen during the 2013 December and 2014 April -ray flares of 3C 279. From the pair opacity arguments, the minimum Doppler factor is estimated to be 14 and the location of the -ray emitting region is found to be either at the outer edge of the broad line region or farther out from it.

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