  The high frequency peaked BL Lac object PG 1553+113 underwent a flaring event
in 2012. The High Energy Stereoscopic System (H.E.S.S.) observed this source
for two consecutive nights at very high energies (VHE, $E>$100~GeV). The data
show an increase of a factor of three of the flux with respect to archival
measurements with the same instrument and hints of intra-night variability. The
data set has been used to put constraints on possible Lorentz invariance
violation (LIV), manifesting itself as an energy dependence of the velocity of
light in vacuum, and to set limits on the energy scale at which Quantum Gravity
effects causing LIV may arise. With a new method to combine H.E.S.S. and Fermi
large area telescope data, the previously poorly known redshift of PG 1555+113
has been determined to be close to the value derived from optical measurements.
