  We report on the first completely simultaneous observation of a gamma-ray
burst (GRB) using an array of Imaging Atmospheric Cherenkov Telescopes which is
sensitive to photons in the very-high-energy (VHE) gamma-ray range (>~100 GeV).
On 2006 June 2, the Swift Burst Alert Telescope (BAT) registered an unusually
soft gamma-ray burst (GRB 060602B). The burst position was under observation
using the High Energy Stereoscopic System (H.E.S.S.) at the time the burst
occurred. Data were taken before, during, and after the burst. A total of 5
hours of observations were obtained during the night of 2006 June 2-3, and 5
additional hours were obtained over the next 3 nights. No VHE gamma-ray signal
was found during the period covered by the H.E.S.S. observations. The 99%
confidence level flux upper limit (>1 TeV) for the prompt phase (9s) of GRB
060602B is 2.9x10^-9 erg cm^-2 s^-1. Due to the very soft BAT spectrum of the
burst compared to other Swift GRBs and its proximity to the Galactic center,
the burst is likely associated with a Galactic X-ray burster, although the
possibility of it being a cosmological GRB cannot be ruled out. We discuss the
implications of our flux limits in the context of these two bursting scenarios.
