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-β (0νββ) decay, a matter-creating process without the balancing emission of antimatter. The GERDA Collaboration searches for the 0νββ decay of 76Ge 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 T1/2 > 0.9 × 1026 years (90% C.L.). Our T1/2 sensitivity, assuming no signal, is 1.1 × 1026 years. Combining the latter with those from other 0νββ decay searches yields a sensitivity to the effective Majorana neutrino mass of 0.07 to 0.16 electron volts.