A discovery that neutrinos are Majorana fermions would have profound implications for particle physics and cosmology. The Majorana character of neutrinos would make possible the neutrinoless double-beta (0 nu beta beta) decay, a matter-creating process without the balancing emission of antimatter. The GERDA Collaboration searches for the 0 nu beta beta decay of Ge-76 by operating bare germanium detectors in an active liquid argon shield. With a total exposure of 82.4 kg.year, we observe no signal and derive a lower half-life limit of T-1/2 > 0.9 x 10(26) years (90% C.L.). Our T-1/2 sensitivity, assuming no signal, is 1.1 x 10(26) years. Combining the latter with those from other 0 nu beta beta decay searches yields a sensitivity to the effective Majorana neutrino mass of 0.07 to 0.16 electron volts.