  We present results from a blind, spectroscopic survey for redshift ~5.7
Lyman-alpha-emitting galaxies using the Inamori Magellan Areal Camera and
Spectrograph. A total of ~200 square arcminutes were observed in the COSMOS and
LCIRS fields using a narrowband filter, which transmits between atmospheric
emission lines at 8190 A, and a mask with 100 longslits. This observing
technique provides higher emission-line sensitivity than narrowband imaging and
probes larger volumes than strong lensing. We find 170 emission-line galaxies
and identify their redshifts spectroscopically. We confirm three Lyman-alpha
emitting galaxies (LAEs), the first discovered using multislit-narrowband
spectroscopy. Their line profiles are narrow, but fitted models suggest
instrinsic, unattenuated widths 400 km/s FWHM. The red wing of the line
profiles present features consistent with galactic winds. The star formation
rates of these galaxies are at least 5-7 Msun/yr and likely a factor of two
higher. We estimate the number density of L .ge. 5e42 erg/s LAEs is
9.0(+12,-4)e-5 Mpc-3 at redshift 5.7 and constrain the Schechter function
parameters describing this population. Galaxies fainter than our detection
limit may well be the primary source of ionizing photons at redshift ~ 6. We
argue, however, that the break luminosity L* is not yet well constrained. If
this break luminosity is near our detection limit, and somewhat lower than
previous estimates, then the detected LAE population could be responsible for
ionizing the intergalactic gas at redshift ~6. We discuss the potential of
multislit-narrowband spectroscopy for deeper emission-line surveys.
