Theoretical calculations predict 270Hs (Z=108, N=162) to be a doubly magic deformed nucleus, decaying mainly by alpha-particle emission. In this work, based on a rapid chemical isolation of Hs isotopes produced in the 26Mg+248Cm reaction, we observed 15 genetically linked nuclear decay chains. Four chains were attributed to the new nuclide 270Hs, which decays by alpha-particle emission with Qalpha=9.02+/-0.03 MeV to 266Sg which undergoes spontaneous fission with a half-life of 444(-148)(+444) ms. A production cross section of about 3 pb was measured for 270Hs. Thus, 270Hs is the first nucleus for which experimental nuclear decay properties have become available for comparison with theoretical predictions of the N=162 shell stability.