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 22.3h. Point-like very-high-energy (VHE; E>100GeV) $gamma$-ray emission is detected from a source centred on the 1ES 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 $Gamma=3.40pm0.66_{text{stat}}pm0.20_{text{sys}}$ and an integral flux $Phi(E>200GeV) = (3.11pm0.71_{rm stat}pm0.62_{rm sys})times10^{-12} cm^{-2} s^{-1}$, which corresponds to 1.1$%$ of the Crab nebula flux above 200 GeV. Multi-wavelength data obtained with Fermi LAT, Swift XRT and UVOT, RXTE PCA, ATOM, and additional data from WISE, GROND and Catalina, are also used to characterise the broad-band non-thermal emission of 1ES 2322-409. The multi-wavelength 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 synchrotron-self-Compton (SSC) 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.
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