We selected 40 candidate Lyman Alpha Emitting galaxies ( LAEs ) at z \simeq 3.1 with observed frame equivalent widths > 150Å and inferred emission line fluxes > 2.5 \times 10 ^ { -17 } ergs cm ^ { -2 } s ^ { -1 } from deep narrow-band and broad-band MUSYC images of the Extended Chandra Deep Field South . Covering 992 arcmin ^ { 2 } , this is the largest “ blank field ” surveyed for LAEs at z \sim 3 , allowing an improved estimate of the space density of this population of 3 \pm 1 \times 10 ^ { -4 } h _ { 70 } ^ { 3 } Mpc ^ { -3 } . Spectroscopic follow-up of 23 candidates yielded 18 redshifts , all at z \simeq 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 \simeq 27 and very blue continuum colors , ( V - z ) \simeq 0 . Over 80 % of the LAEs have the right UVR colors to be selected as Lyman break galaxies , but only 10 % also have R \leq 25.5 . Stacking the UBVRIzJK fluxes reveals that LAEs have stellar masses \simeq 5 \times 10 ^ { 8 } h _ { 70 } ^ { -2 } M _ { \odot } and minimal dust extinction , A _ { V } \lesssim 0.1 . Inferred star formation rates are \simeq 6 h _ { 70 } ^ { -2 } M _ { \odot } yr ^ { -1 } , yielding a cosmic star formation rate density of 2 \times 10 ^ { -3 } h _ { 70 } M _ { \odot } yr ^ { -1 } Mpc ^ { -3 } . None of our LAE candidates show evidence for rest-frame emission line equivalent widths EW _ { rest } > 240Å which might imply a non-standard IMF . One candidate is detected by Chandra , implying an AGN fraction of 2 \pm 2 % for LAE candidate samples . In summary , LAEs at z \sim 3 have rapid star formation , low stellar mass , little dust obscuration and no evidence for a substantial AGN component . Based on observations obtained with the Magellan telescopes at Las Campanas Observatory and at Cerro Tololo Inter-American Observatory , a division of the National Optical Astronomy Observatories , which is operated by the Association of Universities for Research in Astronomy , Inc. under cooperative agreement with the National Science Foundation .