Single-chain polymeric nanoparticles (SCPNs) have been extensively explored as a synthetic alternative to enzymes for catalytic applications. However, the inherent structural heterogeneity of SCPNs, arising from the dispersity of the polymer backbone and stochastic incorporation of different monomers as well as catalytic moieties, is expected to lead to variations in catalytic activity between individual particles. To understand the effect of structural heterogeneities on the catalytic performance of SCPNs, techniques are required that permit researchers to directly monitor SCPN activity at the single-polymer level. In this study, we introduce the use of single-molecule fluorescence microscopy to study the kinetics of Cu(I)-containing SCPNs towards depropargylation reactions. We developed Cu(I)-containing SCPNs that exhibit fast kinetics towards depropargylation and Cu-catalyzed azide-alkyne click reactions, making them suitable for single-particle kinetic studies. SCPNs were then immobilized on the surface of glass coverslips and the catalytic reactions were monitored at a single-particle level using total internal reflection fluorescence (TIRF) microscopy. Our studies revealed the interparticle turnover dispersity for Cu(I)-catalyzed depropargylations. In the future, our approach can be extended to different polymer designs which can give insights into the intrinsic heterogeneity of SCPN catalysis and can further aid in the rational development of SCPN-based catalysts.