We selected 40 candidate Ly alpha-emitting galaxies ( LAEs) at z similar or equal to 3.1 with observed-frame equivalent widths greater than 150 and inferred emission-line fluxes above 2.5 x 10(-17) ergs cm(-2) s(-1) 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 similar to 3, allowing an improved estimate of the space density of this population of ( 3 +/- 1) x 10(-4) h(70)(3) Mpc(-3). Spectroscopic follow-up of 23 candidates yielded 18 redshifts, all at z similar or equal to 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 similar or equal to 27 and very blue continuum colors, V-z similar or equal to 0. Over 80% of the LAEs have the right UVR colors to be selected as LBGs, but only 10% also have R <= 25.5. Stacking the UBVRIzJK fluxes reveals that LAEs have stellar masses similar or equal to 5 x 10(8) h(70)(-2) M-circle dot and minimal dust extinction, A(V) less than or similar to 0.1. Inferred star formation rates are similar or equal to 6 h(70)(-2) M-circle dot yr(-1), yielding a cosmic star formation rate density of 2 x 10(-3) h(70) M-circle dot yr(-1) Mpc(-3). None of our LAE candidates show evidence for rest-frame emission-line equivalent widths EWrest > 240 (A) over circle that might imply a nonstandard initial mass function. One candidate is detected by Chandra, implying an AGN fraction of 2% +/- 2% for LAE candidate samples. In summary, LAEs at z similar to 3 have rapid star formation, low stellar mass, little dust obscuration, and no evidence for a substantial AGN component.