  Out of several dozen z > 7 candidate galaxies observed spectroscopically,
only five have been confirmed via Lyman-alpha emission, at z=7.008, 7.045,
7.109, 7.213 and 7.215. The small fraction of confirmed galaxies may indicate
that the neutral fraction in the intergalactic medium (IGM) rises quickly at z
> 6.5, as Lyman-alpha is resonantly scattered by neutral gas. However, the
small samples and limited depth of previous observations makes these
conclusions tentative. Here we report the results of a deep near-infrared
spectroscopic survey of 43 z > 6.5 galaxies. We detect only a single galaxy,
confirming that some process is making Lyman-alpha difficult to detect. The
detected emission line at 1.0343 um is likely to be Lyman-alpha emission,
placing this galaxy at a redshift z = 7.51, an epoch 700 million years after
the Big Bang. This galaxy's colors are consistent with significant metal
content, implying that galaxies become enriched rapidly. We measure a
surprisingly high star formation rate of 330 Msol/yr, more than a factor of 100
greater than seen in the Milky Way. Such a galaxy is unexpected in a survey of
our size, suggesting that the early universe may harbor more intense sites of
star-formation than expected.
