We investigate the origin of extragalactic continuum emission and its relation to the stellar population of a recently discovered peculiar z=3.344 Lyman alpha emitter. Based on an analysis of the broad-band colors and morphology we find further support for the idea that the underlying galaxy is being fed by a large-scale (L > 35 kpc) accretion stream. Archival HST images show small scale (~5 kpc) tentacular filaments converging near a hot-spot of star-formation, possibly fueled by gas falling in along the filaments. The spectral energy distribution of the tentacles is broadly compatible with either (1) non-ionizing rest-frame far-UV continuum emission from stars formed in an 60 million-year-old starburst; (2) nebular 2-photon-continuum radiation, arising from collisional excitation cooling, or (3) a recombination spectrum emitted by hydrogen fluorescing in response to ionizing radiation escaping from the galaxy. The latter possibility simultaneously accounts for the presence of asymmetric Lyman alpha emission from the large-scale gaseous filament and the nebular continuum in the smaller-scale tentacles as caused by the escape of ionizing radiation from the galaxy. Possible astrophysical explanations for the nature of the tentacles include: a galactic wind powered by the starburst; in-falling gas during cold accretion, or tails of interstellar medium dragged out of the galaxy by satellite halos that have plunged through the main halo. The possibility of detecting extragalactic 2-photon continuum emission in space-based, broad-band images suggests a tool for studying the gaseous environment of high redshift galaxies at much greater spatial detail than possible with Lyman alpha or other resonance line emission.