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We describe the results of an extremely deep, 0.28 deg^2 survey for z = 3.1Ly-alpha emission-line galaxies in the Extended Chandra Deep Field South. Byusing a narrow-band 5000 Anstrom filter and complementary broadband photometryfrom the MUSYC survey, we identify a statistically complete sample of 162galaxies with monochromatic fluxes brighter than 1.5 x 10^-17 ergs cm^-2 s^-1and observers frame equivalent widths greater than 80 Angstroms. We show thatthe equivalent width distribution of these objects follows an exponential witha rest-frame scale length of w_0 = 76 +/- 10 Angstroms. In addition, we showthat in the emission line, the luminosity function of Ly-alpha galaxies has afaint-end power-law slope of alpha = -1.49 +/- 0.4, a bright-end cutoff of logL^* = 42.64 +/- 0.2, and a space density above our detection thresholds of 1.46+/- 0.12 x 10^-3 h70^3 galaxies Mpc^-3. Finally, by comparing the emission-lineand continuum properties of the LAEs, we show that the star-formation ratesderived from Ly-alpha are ~3 times lower than those inferred from therest-frame UV continuum. We use this offset to deduce the existence of a smallamount of internal extinction within the host galaxies. This extinction,coupled with the lack of extremely-high equivalent width emitters, argues thatthese galaxies are not primordial Pop III objects, though they are young andrelatively chemically unevolved.

Ly-alpha Emission-Line Galaxies at z = 3.1 in the Extended Chandra Deep Field South