Antibody light chains can aggregate as amyloid fibrils to cause systemic AL amyloidosis. Amyloid deposition requires unfolding of the light chain from its native state, but the mechanistic details of how this occurs are not fully understood. Inhibiting amyloid formation by stabilizing the precursor light chain proteins against unfolding and proteolysis is a potential therapeutic strategy. Small molecules that bind to the native state of light chains are under development as drug candidates. An important challenge for potential stabilizer drugs is to bind multiple light chains and suppress their dynamics, since every patient has a unique amyloid-forming light chain. Here, we used hydrogen-deuterium exchange measured by mass spectrometry to characterize the binding of six small molecule stabilizers to eleven different λ light chain proteins. Despite structural and dynamic differences among the light chains, the binding of the most efficacious stabilizer molecule led to increased protection from hydrogen exchange, consistent with reduced local and global unfolding. Protection upon binding was most prominent in residues within complementarity determining region 3 and framework region 4 of the light chain variable domains, which undergo major conformational changes upon amyloid formation. Stabilizer binding also reduced the rate at which all light chains were cleaved by protease. These data show how stabilizers can suppress the range of conformational dynamics associated with light chain aggregation, supporting their therapeutic potential.