By using an approach that allows computing the free energy in high-dimensional spaces together with a clustering technique capable of identifying kinetic attractors stabilized by conformational disorder, we analyze a molecular dynamics trajectory of the Villin headpiece from Lindorff-Larsen, K.; et al. How fast-folding proteins fold. 517-520. We compute its free-energy landscape in the space of all its C carbons. This landscape has the shape of a 12-dimensional funnel with the free energy decreasing monotonically as a function of the native contacts. There are no significant folding barriers. The funnel can be partitioned in five regions, three mainly folded and two unfolded, which behave as Markov states. The slowest relaxation time among these states corresponds to the folding transition. The second slowest time is only twice smaller and corresponds to a transition within the unfolded state. This indicates that the unfolded part of the funnel has a nontrivial shape, which induces a sizable kinetic barrier between disordered states.