We report results of a unprecedentedly deep , blind search for Ly \alpha emitters ( LAEs ) at z = 5.7 using IMACS , the Inamori-Magellan Areal Camera & Spectrograph , with the goal of identifying missing sources of reionization that could also be basic building blocks for today ’ s L ^ { * } galaxies . We describe how improvements in wide field imaging with the Baade telescope , upgrades to IMACS , and the accumulation of \sim 20 hours of integration per field in excellent seeing led to the detection of single-emission-line sources as faint as F \approx 2 \hbox { $ \times~ { } 10 ^ { -18 } $ } ergs s ^ { -1 } cm ^ { -2 } , a sensitivity 5 times deeper than our first search ( Martin et al . 2008 ) . A reasonable correction for foreground interlopers implies a steep rise of approximately an order of magnitude in source density for a factor of four drop in flux , from F = 10 ^ { -17.0 } ergs s ^ { -1 } cm ^ { -2 } to F = 10 ^ { -17.6 } ( 2.5 \hbox { $ \times~ { } 10 ^ { -18 } $ } ) ergs s ^ { -1 } cm ^ { -2 } . At this flux the putative LAEs have reached a surface density of \sim 1 per sq arcminute — a comoving volume density of 4 \times 10 ^ { -3 } Mpc ^ { -3 } , several times the density of L* galaxies today . Such a population of faint LAEs would account for a significant fraction of the critical flux density required to complete reionization at this epoch , and would be good candidates for building blocks of stellar mass \sim 10 ^ { 8 - 9 } M _ { \odot } for the young galaxies of this epoch .