  We derive the luminosity function of high-redshift Lyman alpha emitting
sources from a deep, blind, spectroscopic survey that utilized strong-lensing
magnification by intermediate-redshift clusters of galaxies. We observed
carefully selected regions near 9 clusters, consistent with magnification
factors generally greater than 10 for the redshift range 4.5<z<6.7. Eleven
emission-line candidates were located in the range 2.2<z<5.6 whose
identification we justify as Lyman alpha, in most cases via further
spectroscopic observations. The selection function we constructed for our
survey takes into account our varying intrinsic Lyman alpha line sensitivity as
a function of wavelength and sky position. By virtue of the strong
magnification factor, we provide constraints on the Lyman alpha luminosity
function to unprecedented limits of 10^40 erg/s, corresponding to a
star-formation rate of 0.01 Msun/yr. Our cumulative z=5 Lyman alpha luminosity
function is consistent with a power law form, n(>L) proportional to L^-1 over
10^41 to 10^42.5 erg/s. When combined with the results of other surveys,
limited at higher luminosities, our results suggest evidence for the
suppression of star formation in low-mass halos, as predicted in popular models
of galaxy formation.
