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 galaxys 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.
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