In the course of our ongoing search for serendipitous high-redshift Ly \alpha emission in deep archival Keck spectra , we discovered two very high equivalent width ( W _ { \lambda } ^ { obs } \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \mathchar 536 $% } \hss } \raise 2.0 pt \hbox { $ \mathchar 318 $ } } 450 Å , 2 \sigma ) Ly \alpha emission line candidates at z \sim 3 in a moderate dispersion ( \lambda / \Delta \lambda \simeq 1200 ) spectrogram .
Both lines have low velocity dispersions ( \sigma _ { v } \sim 60 { km s ^ { -1 } } ) and deconvolved radii r \approx 1 h _ { 50 } ^ { -1 } kpc .
We argue that the lines are Ly \alpha , and are powered by stellar ionization .
The surface density of robust , high equivalent width Ly \alpha candidates is estimated to be \sim 3 \pm 2 { arcmin } ^ { -2 } per unit redshift at z \simeq 3 , consistent with the estimate of \ @ citex [ ] [ ] Cowie:98 .
The Ly \alpha emission line source characteristics are consistent with the galaxies undergoing their first burst of star formation , i.e. , with being primeval .
Source sizes and velocity dispersions are comparable to the theoretical primeval galaxy model of \ @ citex [ ] [ ] Lin:92 based on the inside-out , self-similar collapse of an isothermal sphere .
In this model , star formation among field galaxies is a protracted process .

Galaxies are thought to be able to display high equivalent widths for only the first \sim few \times 10 ^ { 7 } yr .
This time is short in relation to the difference in look back times between z = 3 and z = 4 , and implies that a substantial fraction of strong line-emitting galaxies at z = 3 were formed at redshifts z \leq 4 .
We discuss the significance of high-equivalent width Ly \alpha -emitting galaxies in terms of the emerging picture of the environment , and the specific characteristics of primeval galaxy formation at high redshift .