  An exceptional $\gamma$-ray outburst from 3C 279 is detected by {\it
Fermi}-Large Area Telescope (LAT) in 2015 June. In the energy range of
0.1$-$300 GeV, the highest flux measured is (39.1$\pm$2.5) $\times$ 10$^{-6}$
\phflux, which is the highest $\gamma$-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 $\gamma$-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 $\sim$1 GeV) which is in contrast to that seen during the 2013
December and 2014 April $\gamma$-ray flares of 3C 279. From the $\gamma\gamma$
pair opacity arguments, the minimum Doppler factor is estimated to be 14 and
the location of the $\gamma$-ray emitting region is found to be either at the
outer edge of the broad line region or farther out from it.
