We selected 40 candidate Ly{alpha}-emitting galaxies (LAEs) at z~3.1 with observed-frame equivalent widths greater than 150{AA} and inferred emission-line fluxes above 2.5x10^-17^ergs/cm^2^/s from deep narrowband and broadband MUSYC images of the Extended Chandra Deep Field South. Covering 992-arcmin^2^, this is the largest "blank field" surveyed for LAEs at z~3, allowing an improved estimate of the space density of this population of (3+/-1)x10^4^h/Mpc^3^. Spectroscopic follow-up of 23 candidates yielded 18 redshifts, all at z~3.1. Over 80% of the LAEs are dimmer in continuum magnitude than the typical Lyman break galaxy (LBG) spectroscopic limit of R=25.5 (AB), with a median continuum magnitude R~27 and very blue continuum colors, V-z~=0.