  The serendipitous discovery of an unidentified extended TeVgamma-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 deg 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 +- 0.02) deg and the integral flux
above 380 GeV is compatible with constant emission over the entire
observational period of (17 +- 3)% of the Crab Nebula flux. The measured energy
spectrum can be described by a power-law dN/dE ~ E^-Gamma with a photon index
of Gamma = 2.44 +- 0.05_stat +- 0.2_syst. Up to now, no counterpart at other
wavelengths is identified. Various possible TeV production scenarios are
discussed.
