Molecular chaperones are key components of the cellular proteostasis network whose role includes the suppression of the formation and proliferation of pathogenic aggregates associated with neurodegenerative diseases. The molecular principles that allow chaperones to recognize misfolded and aggregated proteins remain, however, incompletely understood. To address this challenge, here we probe the thermodynamics and kinetics of the interactions between chaperones and protein aggregates under native solution conditions using a microfluidic platform. We focus on the binding between amyloid fibrils of α-synuclein, associated with Parkinson's disease, to the small heat-shock protein αB-crystallin, a chaperone widely involved in the cellular stress response. We find that αB-crystallin binds to α-synuclein fibrils with high nanomolar affinity and that the binding is driven by entropy rather than enthalpy. Measurements of the change in heat capacity indicate significant entropic gain originates from the disassembly of the oligomeric chaperones that function as an entropic buffer system. These results shed light on the functional roles of chaperone oligomerization and show that chaperones are stored as inactive complexes which are capable of releasing active subunits to target aberrant misfolded species.