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.
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