The atomic mass of 136Xe has been measured by comparing cyclotron frequencies of single ions in a Penning trap. The result, with 1 standard deviation uncertainty, is M(136Xe)=135.907 214 484 (11) u. Combined with previous results for the mass of 136Ba [Audi, Wapstra, and Thibault, Nucl. Phys. A 729, 337 (2003)10.1016/j.nuclphysa.2003.11.003], this gives a Q value (M[136Xe]-M[136Ba])c(2)=2457.83(37) keV, sufficiently precise for ongoing searches for the neutrinoless double-beta decay of 136Xe.