The Hsp70 family of chaperones plays an essential role in suppressing protein aggregation in the cell. Here we investigate the factors controlling the intrinsic ability of human Hsp70 to inhibit the elongation of amyloid fibrils formed by the Parkinson's disease-related protein α-synuclein. Using kinetic analysis, we show that Hsp70 binds preferentially to α-synuclein fibrils as a consequence of variations in the association and dissociation rate constants of binding to the different aggregated states of the protein. Our findings illustrate the importance of the kinetics of binding of molecular chaperones, and also of potential therapeutic molecules, in the efficient suppression of specific pathogenic events linked to neurodegeneration.