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A hotspot at a position compatible with the BL. Lac object 1ES 2322-409 was serendipitously detected with H.E.S.S. during observations performed in 2004 and 2006 on the blazar PKS 2316-423. Additional data on 1ES 2322-409 were taken in 2011 and 2012, leading to a total live-time of 22.3 h. Point-like very-high-energy (VHE; E > 100 GeV) gamma-ray emission is detected from a source centred on the IFS 2322-409 position, with an excess of 116.7 events at a significance of 6.0 sigma. The average VHE gamma-ray spectrum is well described with a power law with a photon index Gamma = 3.40 +/- 0.66(stat) +/- 0.20(sys) and an integral flux Phi(E > 200 GeV) = (3.11 +/- 0.71(stat) 0.62(sys)) x 10(-2)cm(-2)s(-1), which corresponds to 1.1 per cent of the Crab nebula flux above 200 GeV. Multiwavelength data obtained with Fermi LAT, Swift XRT and UVOT, RXTE PCA, ATOM, and additional data from WISE, GROND, and Catalina are also used to characterize the broad-band non-thermal emission of lES 2322-409. The multiwavelength behaviour indicates day-scale variability. Swift UVOT and XRT data show strong variability at longer scales. A spectral energy distribution (SED) is built from contemporaneous observations obtained around a high state identified in Swift data. A modelling of the SED is performed with a stationary homogeneous one-zone synchrotronself-Compton leptonic model. The redshift of the source being unknown, two plausible values were tested for the modelling. A systematic scan of the model parameters space is performed, resulting in a well-constrained combination of values providing a good description of the broad-band behaviour of 1ES 2322-409.