  The extreme synchrotron BL Lac object H2356-309, located at a redshift of z =
0.165, was observed from June to December 2004 with a total exposure of approx.
40 h live-time with the H.E.S.S. (High Energy Stereoscopic System) array of
atmospheric-Cherenkov telescopes (ACTs). Analysis of this data set yields, for
the first time, a strong excess of 453 gamma-rays (10 standard deviations above
background) from H2356-309, corresponding to an observed integral flux above
200 GeV of I(>200GeV) = (4.1+-0.5) 10^12 cm^-2.s^-1 (statistical error only).
The differential energy spectrum of the source between 200 GeV and 1.3 TeV is
well-described by a power law with a normalisation (at 1 TeV) of N_0 = (3.00 +-
0.80_stat +- 0.31_sys) 10^-13 cm^-2.s^-1.TeV^-1 and a photon index of Gamma =
3.09 +- 0.24_stat +- 0.10_sys. H2356-309 is one of the most distant BL Lac
objects detected at very-high-energy gamma-rays so far. Results from
simultaneous observations from ROTSE-III (optical), RXTE (X-rays) and NRT
(radio) are also included and used together with the H.E.S.S. data to constrain
a single-zone homogeneous synchrotron self-Compton (SSC) model. This model
provides an adequate fit to the H.E.S.S. data when using a reasonable set of
model parameters.
