The understanding of amyloid β-peptide (Aβ) interactions with cellular membranes is a crucial molecular challenge against Alzheimer's disease. Indeed, Aβ prefibrillar oligomeric intermediates are believed to be the most toxic species, able to induce cellular damages directly by membrane damage. We present a neutron-scattering study on the interaction of large unilamellar vesicles (LUV), as cell membrane models, with both freshly dissolved Aβ and early toxic prefibrillar oligomers, intermediate states in the amyloid pathway. In addition, we explore the effect of coincubating the Aβ-peptide with the chaperonin Hsp60, which is known to strongly interact with it in its aggregation pattern. In fact, the interaction of the LUV with coincubated Aβ/Hsp60, right after mixing and after following the aggregation protocol leading to the toxic intermediates in the absence of Hsp60, is studied. Neutron spin echo experiments show that the interaction with both freshly dissolved and aggregate Aβ species brings about an increase in membrane stiffness, whereas the presence of even very low amounts of Hsp60 (ratio Aβ/Hsp60 = 25:1) maintains unaltered the elastic properties of the membrane bilayer. A coherent interpretation of these results, related to previous literature, can be based on the ability of the chaperonin to interfere with Aβ aggregation, by the specific recognition of the Aβ-reactive transient species. In this framework, our results strongly suggest that early in a freshly dissolved Aβ solution are present some species able to modify the bilayer dynamics, and the chaperonin plays the role of an assistant in such stochastic "misfolding events", avoiding the insult on the membrane as well as the onset of the aggregation cascade.