Keeping track of the aggregation kinetics of amyloid fibrils is essential for understanding their formation mechanism and eventually developing treatments for misfolded protein-related diseases. A simulation study of a series of A beta(9-40) amyloid fibrils with different size shows that novel two-dimensional near-ultraviolet (2DNUV) spectra contain characteristic signatures of interactions between peptides. Chiral 2DNUV signals show a larger degree of exciton delocalization compared to their nonchiral counterparts. Intensities of specific peaks provide a direct measure of the number of peptides in a fibril. These signals could be used to monitor the fibril growth kinetics, one peptide at a time.