A simple model of classical relaxation in a one-dimensional harmonic potential with a hierarchical distribution of barriers is studied. The vanishing of an effective diffusion constant results in a transition of the low-lying eigenstates of the master equation from extended to localized. For a parameter characterizing the barrier distribution greater than a critical value Rg${R}_{c}$, the low-lying states are extended on the length scale of the equilibrium distribution. For R${R}_{c}$ the low-lying states are sharply localized at the most difficult barriers to cross. The correlation function 〈x(t)x(0)〉 is analyzed in terms of this eigenstate structure. For Rg${R}_{c}$ correlations are shown to decay as a pure exponential for all times. For R${R}_{c}$, decay is a sum of exponentials which asymptotically approaches the stretched exponential form at long times. Numerical simulations are performed to compute the decay of the correlation functions at shorter times. This decay may also be empirically fitted to a stretched exponential form. The relation of the model to anomalous relaxation in glassy systems is discussed.