  We search for high-energy gamma-ray emission from the binary neutron star
merger GW170817 with the H.E.S.S. Imaging Air Cherenkov Telescopes. The
observations presented here have been obtained starting only 5.3h after
GW170817. The H.E.S.S. target selection identified regions of high probability
to find a counterpart of the gravitational wave event. The first of these
regions contained the counterpart SSS17a that has been identified in the
optical range several hours after our observations. We can therefore present
the first data obtained by a ground-based pointing instrument on this object. A
subsequent monitoring campaign with the H.E.S.S. telescopes extended over
several days, covering timescales from 0.22 to 5.2 days and energy ranges
between $270\,\mathrm{GeV}$ to $8.55\,\mathrm{TeV}$. No significant gamma-ray
emission has been found. The derived upper limits on the very-high-energy
gamma-ray flux for the first time constrain non-thermal, high-energy emission
following the merger of a confirmed binary neutron star system.
