  We present a rest-frame ultraviolet morphological analysis of 78 resolved,
high S/N z ~ 3.1 Lyman Alpha Emitters (LAEs) in the Extended Chandra Deep Field
South (ECDF-S). Using HST/ACS V -band images taken as part of the GEMS, GOODS,
and HUDF surveys. For each LAE system identified via our ground-based
narrow-band imaging, we have identified those LAE systems with multiple
components. We measure the concentration index and present the results of our
GALFIT fits for ellipticity, Sersic index, and sizes for each resolved
component with S/N > 30 as well as for each LAE system with S/N > 30. The LAEs
show a heterogeneous distribution of morphologies while the ma jority tend to
be highly concentrated and compact in size. We only measure the morphological
properties of resolved LAEs. For systems showing multiple components we also
measured the morphology of the individual components. The resolved LAEs are
highly concentrated (2 < C < 4) and show a similar distribution to that
measured for stars, suggesting that this diagnostic is a poor discriminator
near the resolution limit. The measured ellipticities for components show a
distribution peaked at {\epsilon} ~ 0.55 which is significantly different from
the flat distribution of ellipticities observed for local spiral galaxies and
is similar to the distribution found for Lyman-break galaxies at the same
redshift. There is a wide range of best-fit Sersic indices (1 < n < 10) with
the majority being between 0 < n < 2. The distribution is similar to the
distribution of Sersic indices seen locally. A visual inspection of the images
suggests a qualitative morphological transition at n ~ 2, with small-n LAEs
having extended or multimodal light distributions and relatively little diffuse
emission and large-n LAEs have compact central components surrounded by diffuse
emission.
