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 _ { 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 } Å . 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 Å 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 .