The superheavy element with atomic number Z=117 was produced as an evaporation residue in the (48)Ca+(249)Bk fusion reaction at the gas-filled recoil separator TASCA at GSI Darmstadt, Germany. The radioactive decay of evaporation residues and their α-decay products was studied using a detection setup that allowed measuring decays of single atomic nuclei with half-lives between sub-μs and a few days. Two decay chains comprising seven α decays and a spontaneous fission each were identified and are assigned to the isotope (294)117 and its decay products. A hitherto unknown α-decay branch in (270)Db (Z = 105) was observed, which populated the new isotope (266)Lr (Z = 103). The identification of the long-lived (T(1/2) = 1.0(-0.4)(+1.9) h) α-emitter (270)Db marks an important step towards the observation of even more long-lived nuclei of superheavy elements located on an "island of stability."