We selected 40 candidate Lyman Alpha Emitting galaxies (LAEs) at z ~=3.1 with observed frame equivalent widths >150A and inferred emission line fluxes >2.5x10^-17 ergs/cm^2/s from deep narrow-band and broad-band MUSYC images of the Extended Chandra Deep Field South. Covering 992 sq. arcmin, 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+-1x10^-4 h_70^3/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 spectroscopic limit of R= 25.5 (AB), with a median continuum magnitude R ~=27 and very blue continuum colors, (V-z) ~=0. Over 80% of the LAEs have the right UVR colors to be selected as Lyman break galaxies, but only 10% also have R<=25.5. Stacking the UBVRIzJK fluxes reveals that LAEs have stellar masses ~=5x10^8 h_70^-2 M_sun and minimal dust extinction, A_V < ~ 0.1. Inferred star formation rates are ~=6 h_70^-2 M_sun/yr, yielding a cosmic star formation rate density of 2x10^-3 h_70 M_sun/yr/Mpc^3. None of our LAE candidates show evidence for rest-frame emission line equivalent widths EW_rest>240A which might imply a non-standard IMF. One candidate is detected by Chandra, implying an AGN fraction of 2+-2% for LAE candidate samples. In summary, LAEs at z ~ 3 have rapid star formation, low stellar mass, little dust obscuration and no evidence for a substantial AGN component.
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