We present the results of a high-spatial-resolution study of the line emission in a sample of z=3.1 Lyman-Alpha-Emitting Galaxies (LAEs) in the Extended Chandra Deep Field-South. Of the eight objects with coverage in our HST/WFPC2 narrow-band imaging, two have clear detections and an additional two are barely detected (~2-sigma). The clear detections are within ~0.5 kpc of the centroid of the corresponding rest-UV continuum source, suggesting that the line-emitting gas and young stars in LAEs are spatially coincident. The brightest object exhibits extended emission with a half-light radius of ~1.5 kpc, but a stack of the remaining LAE surface brightness profiles is consistent with the WFPC2 point spread function. This suggests that the Lyman Alpha emission in these objects originates from a compact (<~2 kpc) region and cannot be significantly more extended than the far-UV continuum emission (<~1 kpc). Comparing our WFPC2 photometry to previous ground-based measurements of their monochromatic fluxes, we find at 95% (99.7%) confidence that we cannot be missing more than 22% (32%) of the Lyman Alpha emission.
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