1RXS J101015.9-311909 is a galaxy located at a redshift of z=0.14 hosting an active nucleus belonging to the class of bright BL Lac objects. Observations at high (HE, E > 100 MeV) and very high (VHE, E > 100 GeV) energies provide insights into the origin of very energetic particles present in such sources and the radiation processes at work. We report on results from VHE observations performed between 2006-10 with H.E.S.S. H.E.S.S. data have been analysed with enhanced analysis methods, making the detection of faint sources more significant. VHE emission at a position coincident with 1RXS J101015.9-311909 is detected with H.E.S.S. for the first time. In a total good-quality livetime of about 49 h, we measure 263 excess counts, corresponding to a significance of 7.1sigma. The photon spectrum above 0.2 TeV can be described by a power-law with a photon index of Gamma = 3.08pm0.42_{stat}pm0.20_{sys}. The integral flux above 0.2 TeV is about 0.8% of the flux of the Crab nebula and shows no significant variability over the time reported. In addition, public Fermi/LAT data are analysed to search for high energy emission from the source. The Fermi/LAT HE emission is significant at 8.3sigma in the chosen 25-month dataset. UV and X-ray contemporaneous observations with the Swift satellite in May 2007 are also reported, together with optical observations performed with the ATOM telescope located at the H.E.S.S. site. Swift observations reveal an absorbed X-ray flux of F_{0.3-7 keV} = 1.04^{+0.04}_{-0.05} times 10^{-11} erg.cm^{-2}.s^{-1} in the 0.3-7 keV range. Finally, all the available data are used to study the sources multi-wavelength properties. The SED can be reproduced using a simple one-zone SSC model with emission from a region with a Doppler factor of 30 and a magnetic field between 0.025 and 0.16 G. These parameters are similar to those obtained for other sources of this type.
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