  In June 2015, the Flat Spectrum Radio Quasar 3C 279 underwent an extremely
bright gamma-ray flare, with an increase of the flux above 100 MeV by a factor
10 in less than 1 day, revealing an intrinsic variability timescale of 2
minutes as detected by the Fermi-LAT. We present results of target of
opportunity observations with the H.E.S.S. experiment on this source over the
nights around the peak of the outburst. The H.E.S.S. data were analysed with
mono and stereo chains. Thanks to the extreme brightness of the source at GeV
energies, it was possible to obtain data from Fermi-LAT, strictly simultaneous
to the H.E.S.S. observation. Simultaneous and quasi-simultaneous observations
at optical and X-ray energies were gathered to reconstruct the multi-wavelength
spectrum helping to constrain theoretical models describing the flare. The
H.E.S.S. observation during the second night, using H.E.S.S. II MONO data, lead
to a clear detection of the source in about 3 hours of live-time. The H.E.S.S.
results were also used to derive limits on the Quantum Gravity scale under the
assumption of Lorentz Invariance Violation. Furthermore, since FSRQs possess
intense optical photon fields surrounding the central region near the black
hole, the VHE data allows constraints on the location of the emitting region to
be derived in order that internal absorption be avoided. The detection of VHE
emission from the powerful flare of the FSRQ 3C 279 by H.E.S.S. II can provide
unique insights into the physical properties of this class of blazar, thanks in
part to the presence of simultaneous and quasi-simultaneous datasets at other
wavelengths. Due to the high redshift of the source (z=0.54), it was also
possible to derive strong constraints on the Quantum Gravity mass scale.
