  When galaxy formation started in the history of the Universe remains unclear.
Studies of the cosmic microwave background indicate that the Universe, after
initial cooling (following the Big Bang), was reheated and reionized by hot
stars in newborn galaxies at a redshift in the range 6 < z < 14 (ref. 1).
Though several candidate galaxies at redshift z > 7 have been identified
photometrically (refs 2,3), galaxies with spectroscopically confirmed redshifts
have been confined to z < 6.6 (refs. 4-8). Here we report a spectroscopic
redshift of z = 6.96 (corresponding to just 750 Myr after the Big Bang) for a
galaxy whose spectrum clearly shows Lyman-alpha emission at 9,682 A, indicating
active star formation at a rate of about 10 M_sun/yr, where M_sun us the mass
of the Sun. This demonstrates that galaxy formation was under way when the
Universe was only about 6 per cent of its present age. The number density of
galaxies at z = 7 seems to be only 18-36 per cent of the density at z = 6.6.
