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We measure the mass of the eta' meson using psi(2S)--> pi+ pi- J/psi,J/psi--> gamma eta' events acquired with the CLEO-c detector operating at theCESR e+e- collider. Using three decay modes, eta'--> rho0 gamma, eta'--> pi+pi- eta with eta--> gamma gamma, and eta'--> pi+ pi- eta with eta--> pi+ pi-pi0, we find M(eta') = 957.793 +- 0.054 +- 0.036 MeV, in which the firstuncertainty is statistical and the second is systematic. This result isconsistent with but substantially more precise than the current world average.

Measurement of the eta'-meson mass using J/psi--> gamma eta'