  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 the
CESR 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 first
uncertainty is statistical and the second is systematic. This result is
consistent with but substantially more precise than the current world average.
