Multiple sclerosis is a progressive neurological disorder that results in the degradation of myelin sheaths that insulate axons in the central nervous system. Therefore promotion of myelin repair is a major thrust of multiple sclerosis treatment research. Two mouse monoclonal natural autoantibodies, O1 and O4, promote myelin repair in several mouse models of multiple sclerosis. Natural autoantibodies are generally polyreactive and predominantly of the IgM isotype. The prevailing paradigm is that because they are polyreactive, these antibodies bind antigens with low affinities. Despite their wide use in neuroscience and glial cell research, however, the affinities and kinetic constants of O1 and O4 antibodies have not been measured to date. In this work, we developed a membrane biosensing platform based on surface plasmon resonance in gold nanohole arrays with a series of surface modification techniques to form myelin-mimicking lipid bilayer membranes to measure both the association and dissociation rate constants for O1 and O4 antibodies binding to their myelin lipid antigens. The ratio of rate constants shows that O1 and O4 bind to galactocerebroside and sulfated galactocerebroside, respectively, with unusually small apparent dissociation constants (KD ≈ 0.9 nM) for natural autoantibodies. This is approximately one to 2 orders of magnitude lower than typically observed for the highest affinity natural autoantibodies. We propose that the unusually high affinity of O1 and O4 to their targets in myelin contributes to the mechanism by which they signal oligodendrocytes and induce central nervous system repair.