Keck/MOSFIRE Spectroscopy of z=7-8 Galaxies: Ly$\alpha$ Emission from a
  Galaxy at z=7.66
  We report the results from some of the deepest Keck/Multi-Object Spectrometer
For Infra-Red Exploration data yet obtained for candidate $z \gtrsim 7$
galaxies. Our data show one significant line detection with 6.5$\sigma$
significance in our combined 10 hr of integration which is independently
detected on more than one night, thus ruling out the possibility that the
detection is spurious. The asymmetric line profile and non-detection in the
optical bands strongly imply that the detected line is Ly$\alpha$ emission from
a galaxy at $z$(Ly$\alpha)=7.6637 \pm 0.0011$, making it the fourth
spectroscopically confirmed galaxy via Ly$\alpha$ at $z>7.5$. This galaxy is
bright in the rest-frame ultraviolet (UV; $M_{\rm UV} \sim -21.2$) with a
moderately blue UV slope ($\beta=-2.2^{+0.3}_{-0.2}$), and exhibits a
rest-frame Ly$\alpha$ equivalent width of EW(Ly$\alpha$) $\sim
15.6^{+5.9}_{-3.6}$ \AA. The non-detection of the 11 other $z \sim$ 7-8
galaxies in our long 10 hr integration, reaching a median 5$\sigma$ sensitivity
of 28 \AA\ in the rest-frame EW(Ly$\alpha$), implies a 1.3$\sigma$ deviation
from the null hypothesis of a non-evolving distribution in the rest-frame
EW(Ly$\alpha$) between $3<z<6$ and $z=$ 7-8. Our results are consistent with
previous studies finding a decline in Ly$\alpha$ emission at $z>6.5$, which may
signal the evolving neutral fraction in the intergalactic medium at the end of
the reionization epoch, although our weak evidence suggests the need for a
larger statistical sample to allow for a more robust conclusion.
