We discuss new observational constraints on the abundance of faint high-redshift Ly? emitters secured from a deep Keck near-infrared spectroscopic survey that utilizes the strong magnification provided by lensing galaxy clusters. In each of nine clusters, we have undertaken a systematic ``blind'' search for line emission with NIRSPEC in the J band within carefully selected regions that offer very high magnifications (>~10×-50×) for background sources with redshifts z~=10. The high magnification enables the detection of emission at unprecedented flux limits (1041-1042 ergs s-1). As the comoving volumes probed are small, our survey is designed to address the important question of whether low-luminosity galaxies could provide the dominant ionizing flux at z~10. Our survey has yielded six promising (>5 ?) candidate Ly? emitters that lie between z=8.7 and z=10.2. We carefully discuss the validity of our detections and the likelihood that the detected line is Ly? in light of earlier, apparently false, claims. Lower redshift line interpretations can be excluded, with reasonable assumptions, through the nondetection of secondary emission in further spectroscopy undertaken with LRIS and NIRSPEC. Nonetheless, as a result of our tests, we argue that at least two of our candidates are likely to be at z~=10. Given the small survey volume, this suggests there is a large abundance of low-luminosity star-forming sources at z~=8-10. While the predicted reionization photon budget depends upon a large number of physical assumptions, our first glimpse at the z~=10 universe suggests that low-luminosity star-forming galaxies contribute a significant proportion of the UV photons necessary for cosmic reionization.