Searches for neutrinoless double beta decays could determine if neutrinos are Majorana particles and could measure their absolute mass scale. The initial stage of the Enriched Xenon Observatory project, EXO-200, will look for two-neutrino and neutrinoless double-beta decays of Xe-136 in a liquid-xenon time-projection chamber. By combining the ionization signal with detection of the scintillation light collected in Large Area Avalanche Photodiodes (LAAPDs), an energy resolution of about 1.4% at the decay energy can be...