Very high-energy gamma-ray emission from PKS 0447-439 was detected with the H.E.S.S. Cherenkov telescope array in December 2009. This blazar is one of the brightest extragalactic objects in the Fermi Bright Source List and has a hard spectrum in the MeV to GeV range. In the TeV range, a photon index of 3.89 +- 0.37 (stat) +- 0.22 (sys) and a flux normalisation at 1 TeV, Phi(1 TeV) = (3.5 +- 1.1 (stat) +- 0.9 (sys)) x 10^{-13} cm^{-2} s^{-1} TeV^{-1}, were found. The detection with H.E.S.S. triggered observations in the X-ray band with the Swift and RXTE telescopes. Simultaneous UV and optical data from Swift UVOT and data from the optical telescopes ATOM and ROTSE are also available. The spectrum and light curve measured with H.E.S.S. are presented and compared to the multi-wavelength data at lower energies. A rapid flare is seen in the Swift XRT and RXTE data, together with a flux variation in the UV band, at a time scale of the order of one day. A firm upper limit of z < 0.59 on the redshift of PKS 0447-439 is derived from the combined Fermi-LAT and H.E.S.S. data, given the assumptions that there is no upturn in the intrinsic spectrum above the Fermi-LAT energy range and that absorption on the Extragalactic Background Light (EBL) is not weaker than the lower limit provided by current models. The spectral energy distribution is well described by a simple one-zone Synchrotron Self-Compton (SSC) scenario, if the redshift of the source is less than z <~ 0.4.
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