The prompt gamma-ray emission from gamma-ray bursts (GRBs) should be detectable out to distances of z > 10 (ref. 1), and should therefore provide an excellent probe of the evolution of cosmic star formation, reionization of the intergalactic medium, and the metal enrichment history of the Universe. Hitherto, the highest measured redshift for a GRB has been z = 4.50 (ref. 5). Here we report the optical spectrum of the afterglow of GRB 050904 obtained 3.4 days after the burst; the spectrum shows a clear continuum at the long-wavelength end of the spectrum with a sharp cut-off at around 9,000 A due to Lyman alpha absorption at z approximately 6.3 (with a damping wing). A system of absorption lines of heavy elements at z = 6.295 +/- 0.002 was also detected, yielding the precise measurement of the redshift. The Si ii fine-structure lines suggest a dense, metal-enriched environment around the progenitor of the GRB.