The proteomes of cells, tissues, and organisms reflect active cellular processes and change continuously in response to intracellular and extracellular cues. Deep, quantitative profiling of the proteome, especially if combined with mRNA and metabolite measurements, should provide an unprecedented view of cell state, better revealing functions and interactions of cell components. Molecular diagnostics and biomarker discovery should benefit particularly from the accurate quantification of proteomes, since complex diseases like cancer change protein abundances and modifications. Currently, shotgun mass spectrometry is the primary technology for high-throughput protein identification and quantification; while powerful, it lacks high sensitivity and coverage. We draw parallels with next-generation DNA sequencing and propose a strategy, termed fluorosequencing, for sequencing peptides in a complex protein sample at the level of single molecules. In the proposed approach, millions of individual fluorescently labeled peptides are visualized in parallel, monitoring changing patterns of fluorescence intensity as N-terminal amino acids are sequentially removed, and using the resulting fluorescence signatures (fluorosequences) to uniquely identify individual peptides. We introduce a theoretical foundation for fluorosequencing and, by using Monte Carlo computer simulations, we explore its feasibility, anticipate the most likely experimental errors, quantify their potential impact, and discuss the broad potential utility offered by a high-throughput peptide sequencing technology.