  We discuss new observational constraints on the abundance of faint high
redshift Lyman-alpha emitters secured from a deep Keck near-infrared
spectroscopic survey which utilizes the strong magnification provided by
lensing galaxy clusters at intermediate redshift (z=0.2-0.5). In each of 9
clusters we have undertaken a systematic `blind' search for line emission with
NIRSPEC in the J-band within carefully-selected regions which offer very high
magnifications (>10-50x) for background sources with redshifts z~10. The high
magnification enables the detection of emission at unprecedented limits (10^41
- 10^42 erg/s), much fainter than those of conventional narrow band imaging and
other spectroscopic searches. As the comoving volumes probed are small, our
survey is designed to address the important question of whether intrinsically
feeble star forming galaxies could provide the dominant ionizing flux at z~10.
Our survey has yielded six promising (>5 sigma) candidate Lyman-alpha emitters
which lie between z=8.7 and z=10.2. 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. [Abridged]
