The connection between free-energy surfaces and chevron plots has been investigated in a laser temperature jump kinetic study of a small ultrafast folding protein, the 35-residue subdomain from the villin headpiece. Unlike all other proteins that have been studied so far, no measurable dependence of the unfolding/refolding relaxation rate on denaturant concentration was observed over a wide range of guanidinium chloride concentration. Analysis with a simple Ising-like theoretical model shows that this denaturant-invariant relaxation rate can be explained by a large movement of the major free energy barrier, together with a denaturant- and reaction coordinate-dependent diffusion coefficient.