The lifetime broadening of the frustrated translation (T) mode parallel to the surface of isolated CO molecules [less than or similar to 6% of a c(2x2) coverage] chemisorbed on Cu(001) has been studied with high resolution inelastic helium atom scattering as a function of the surface temperature and the parallel momentum transfer. The T excitation peak shows a temperature dependent peak shift and a broadening. The latter is attributed to a quartic anharmonic potential contribution described by a spectroscopic constant chi(e) = -0.0085 +/- 0.O008. The extrapolated T-s = 0 K peak broadening is then gamma(0) = 85 +/- 5 mu eV, corresponding to a vibrational lifetime tau = 8 +/- 1 ps. We attribute this lifetime to substrate phonon mediated damping and electronic damping.