Context : Aims : Our aim is to study the production mechanism for very-high-energy ( VHE ; > 100 GeV ) \gamma -rays in distant active galactic nuclei ( AGN ) and use the observed VHE spectrum to derive limits on the Extragalactic Background Light ( EBL ) . We also want to determine physical quantities through the modeling of the object ’ s broad-band spectral energy distribution ( SED ) . Methods : VHE observations ( \sim 25 h live time ) of the BL Lac 1ES 0347-121 ( redshift z = 0.188 ) were conducted with the High Energy Stereoscopic System ( H.E.S.S . ) between August and December 2006 . Contemporaneous X-ray and UV/optical observations from the SWIFT satellite are used to interpret the SED of the source in terms of a synchrotron self Compton ( SSC ) model . Results : An excess of 327 events , corresponding to a statistical significance of 10.1 standard deviations , is detected from 1ES 0347-121 . Its photon spectrum , ranging from \sim 250 GeV to \sim 3 TeV , is well described by a power law with a photon index of \Gamma = 3.10 \pm 0.23 _ { \mathrm { stat } } \pm 0.10 _ { \mathrm { sys } } . The integral flux above 250 GeV corresponds to \sim 2 % of the flux of the Crab Nebula above the same threshold . No VHE flux variability is detected within the data set . Conclusions : Constraints on the EBL density at optical to near-infrared wavelengths derived from the photon spectrum of 1ES 0347-121 are close to the strongest limits derived previously . The strong EBL limits confirm earlier findings , that the EBL density in the near-infrared is close to the lower limits from source counts . This implies that the universe is more transparent to VHE \gamma -rays than previously believed . An SSC model provides a reasonable description of the contemporaneous SED .