The mechanisms linking deposits of insoluble amyloid fibrils to the debilitating neuronal cell death characteristic of neurodegenerative diseases remain enigmatic. Recent findings implicate transiently formed intermediates of mature amyloid fibrils as the principal toxic agent. Hence, determining which intermediate aggregates represent on-pathway precursors or off-pathway side branches is critical for understanding amyloid self-assembly, and for devising therapeutic approaches targeting relevant toxic species. We examined amyloid fibril self-assembly in acidic solutions, using the model protein hen egg-white lysozyme. Combining in situ dynamic light scattering with calibrated atomic-force microscopy, we monitored the nucleation and growth kinetics of multiple transient aggregate species, and characterized both their morphologies and physical dimensions. Upon incubation at elevated temperatures, uniformly sized oligomers formed at a constant rate. After a lag period of several hours, protofibrils spontaneously nucleated. The nucleation kinetics of protofibrils and the tight match of their widths and heights with those of oligomers imply that protofibrils both nucleated and grew via oligomer fusion. After reaching several hundred nanometers in length, protofibrils assembled into mature fibrils. Overall, the amyloid fibril assembly of lysozyme followed a strict hierarchical aggregation pathway, with amyloid monomers, oligomers, and protofibrils forming on-pathway intermediates for assembly into successively more complex structures.