Transmission electron diffraction patterns from ultra-thin aromatic and aliphatic organic films at beam energies of 200 eV–1 keV have been recorded in a custom low energy electron transmission (LEET) chamber. A significant reduction of the molecular damage cross-section, measured by fading of diffraction spots, was found for thin films of the aromatic perylene when the beam energy was reduced from 400 to 200 eV. The corresponding measurements for the aliphatic tetracontane showed a smaller “threshold energy” and the differences are discussed. Electron beam damage from other aromatic materials has also been studied at low energy. Comparison of the carbon K shell ionization cross-section and the measured damage cross-sections show that carbon K-shell ionization is strongly correlated with the damage observed in aromatics at beam energies higher than 284 eV. Calculation of the minimum number of unit cells needed for imaging a single molecule, and comparison of calculated elastic with measured damage cross-sections both indicate new possibilities for imaging biomolecules with low energy electrons.