The energetic pulsar PSR B1706-44 and the adjacent supernova remnant (SNR) candidate G 343.1-2.3 were observed by H.E.S.S. during a dedicated observational campaign in 2007. A new source of very-high-energy (VHE; E > 100 GeV) gamma-ray emission, HESS J1708-443, was discovered with its centroid at RA(J2000) = 17h08m10s and Dec(J2000) = -44d21, with a statistical error of 3 arcmin on each axis. The VHE gamma-ray source is significantly more extended than the H.E.S.S. point-spread function, with an intrinsic Gaussian width of 0.29 +/- 0.04 deg. Its energy spectrum can be described by a power law with a photon index Gamma = 2.0 +/- 0.1 (stat) +/- 0.2 (sys). The integral flux measured between 1-10 TeV is ~17% of the Crab Nebula flux in the same energy range. The possible associations with PSR B1706-44 and SNR G343.1-2.3 are discussed.
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