It is shown that, in submonolayer growth at off-normal incidence, even much less than 1% of transfer from the condensation energy of the deposited atoms into adatom motion is sufficient to induce a net adatom current from the illuminated edge of a two-dimensional island to the other edges, thereby breaking the island symmetry. Such a symmetry breaking phenomenon is most pronounced for deposition at grazing incidence. Comparison between our theoretical predictions and existing experimental results confirms the general validity of the model.