  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.
