The atomic mass of Xe136 has been measured by comparing cyclotron frequencies of single ions in a Penning trap. The result, with 1 standard deviation uncertainty, is M(Xe136)=135.907 214 484 (11) u. Combined with previous results for the mass of Ba136 [Audi, Wapstra, and Thibault, Nucl. Phys. A 729, 337 (2003)NUPABL0375-947410.1016/j.nuclphysa.2003.11.003], this gives a Q value (M[Xe136]-M[Ba136])c2=2457.83(37)keV, sufficiently precise for ongoing searches for the neutrinoless double-beta decay of Xe136.