We report the reproducible first-principles folding of the 40 amino-acid, three-helix headpiece of the HIV accessory protein in a recently developed all-atom free-energy force field. Six of 20 simulations using an adapted basin-hopping method converged to better than 3 A backbone rms deviation to the experimental structure. Using over 60 000 low-energy conformations of this protein, we constructed a decoy tree that completely characterizes its folding funnel.