Aggregates of amyloid-β (Aβ) are characteristic of Alzheimer's disease, but there is no consensus as to either the nature of the toxic molecular complex or the mechanism by which toxic aggregates are produced. We report on a novel feature of amyloid-lipid interactions where discontinuities in the lipid continuum can serve as catalytic centers for a previously unseen microscale aggregation phenomenon. We show that specific lipid membrane conditions rapidly produce long contours of lipid-bound peptide, even at sub-physiological concentrations of Aβ. Using single molecule fluorescence, time-lapse TIRF microscopy and AFM imaging we characterize this phenomenon and identify some exceptional properties of the aggregation pathway which make it a likely contributor to early oligomer and fibril formation, and thus a potential critical mechanism in the etiology of AD. We infer that these amyloidogenic events occur only at areas of high membrane curvature, which suggests a range of possible mechanisms by which accumulated physiological changes may lead to their inception. The speed of the formation is in hours to days, even at 1 nM peptide concentrations. Lipid features of this type may act like an assembly line for monomeric and small oligomeric subunits of Aβ to increase their aggregation states. We conclude that under lipid environmental conditions, where catalytic centers of the observed type are common, key pathological features of AD may arise on a very short timescale under physiological concentration.