The self-assembly of normally soluble proteins into fibrillar amyloid structures is associated with a range of neurodegenerative disorders, such as Parkinson's and Alzheimer's diseases. In the present study, we show that specific events in the kinetics of the complex, multistep aggregation process of one such protein, α-synuclein, whose aggregation is a characteristic hallmark of Parkinson's disease, can be followed at the molecular level using optical super-resolution microscopy. We have explored in particular the elongation of preformed α-synuclein fibrils; using two-color single-molecule localization microscopy we are able to provide conclusive evidence that the elongation proceeds from both ends of the fibril seeds. Furthermore, the technique reveals a large heterogeneity in the growth rates of individual fibrils; some fibrils exhibit no detectable growth, whereas others extend to more than ten times their original length within hours. These large variations in the growth kinetics can be attributed to fibril structural polymorphism. Our technique offers new capabilities in the study of amyloid growth dynamics at the molecular level and is readily translated to the study of the self-assembly of other nanostructures.