The extreme synchrotron BL Lac object H 2356-309, located at a redshift of z = 0.165, was observed from June to December 2004 with a total exposure of ≈40 h live-time with the HESS (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 γ-rays (10 standard deviations above background) from H 2356-309, corresponding to an observed integral flux above 200 GeV of I(>200 GeV) = (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 N0 = (4.1 ± 0.5) × 10-13 cm-2 s-1 TeV-1 and a photon index of Γ = 3.09±0.24stat±0.10sys. H 2356-309 is one of the most distant BL Lac objects detected at very-high-energy γ-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 HESS data to constrain a single-zone homogeneous synchrotron self-Compton (SSC) model. This model provides an adequate fit to the HESS data when using a reasonable set of model parameters