The serendipitous discovery of an unidentified extended TeV \gamma -ray source close to the galactic plane named HESS J1303-631 at a significance of 21 standard deviations is reported .
The observations were performed between February and June 2004 with the H.E.S.S .
stereoscopic system of Cherenkov telescopes in Namibia .
HESS J1303-631 was discovered roughly 0.6 \degr north of the binary system PSR B1259-63 / SS 2883 , the target object of the initial observation campaign which was also detected at TeV energies in the same field of view .
HESS J1303-631 is extended with a width of an assumed intrinsic Gaussian emission profile of \sigma = ( 0.16 \pm 0.02 ) \degr and the integral flux above 380 \mathrm { GeV } is compatible with constant emission over the entire observational period of ( 17 \pm 3 ) \% of the Crab Nebula flux .
The measured energy spectrum can be described by a power-law \mathrm { d } N / \mathrm { d } E \sim E ^ { - \Gamma } with a photon index of \Gamma = 2.44 \pm 0.05 _ { \mathrm { stat } } \pm 0.2 _ { \mathrm { syst } } .
Up to now , no counterpart at other wavelengths is identified .
Various possible TeV production scenarios are discussed .