We describe narrowband and spectroscopic searches for emission-line star forming galaxies in the redshift range 3 – 6 with the 10 m Keck II Telescope. These searches yield a substantial population of objects with only a single strong (equivalent width ≫ 10 A) emission line, lying in the 4000 − 850 A range. Spectra of the objects found in narrowband–selected samples at λ ∼ 539 A and ∼ 674 A show that these very high equivalent width emission lines are generally redshifted Lyα λ 121 A at z ∼ 3.4 and 4.5. The density of these emitters above the 5σ detection limit of 1.5 × 10 −17 ergs cm −2 s −1 is roughly 15,000/⊓ ⊔ • /unit z at both z ∼ 3.4 and 4.5. A complementary deeper (1 σ ∼ 10 −18 ergs cm −2 s −1) slit spectroscopic search covering a wide redshift range but a more limited spatial area (200 ⊓ ⊔ ′′) shows such objects can be found over the redshift range z = 3 − 6, with the currently highest redshift detected being at z = 5.64. The Lyα flux distribution can be used to estimate a minimum star formation rate in the absence of reddening of roughly 0.01 M ⊙ Mpc −3 yr −1 (H 0 = 65 km s −1 Mpc −1 , q 0 = 0.5). Corrections for reddening are likely to be no larger than a factor of two, since observed equivalent widths are close to the maximum values obtainable from ionization by a massive star population. Within the still significant uncertainties, the star formation rate from the Lyα–selected sample is comparable to that of the color-break–selected samples at z ∼ 3, but may represent an increasing fraction of the total rates at higher redshifts. This higher-z population can be readily studied with large ground-based telescopes.