In bombardments of U-238 targets with 186-MeV S-34 projectiles we discovered the alpha-decaying nuclide (267)108 with a half-life of 19(-10)(+29) ms, E(alpha) = 9.74 to 9.87 MeV, and a production cross section of about 2.5 pb. The new nuclide was identified by measuring correlations in energy, time, and position to establish genetic links between its implantation in a position-sensitive silicon detector and subsequent alpha decay followed by alpha decays of known descendant nuclides.