T-cells display the remarkable ability to detect single foreign peptides displayed on target cells, while ignoring highly abundant self peptides. This selectivity has been explained by kinetic proofreading in the T-cell receptor (TCR) signaling pathway, which prevents responses to short-lived binding events regardless of their abundance. However, the biochemical mechanisms that drive kinetic proofreading have remained unclear. Here, using computational modeling, we show that these key signaling properties of the TCR pathway can emerge from the dynamics of LAT phosphorylation, diffusion, and condensation following TCR-pMHC binding. In this model, time delays in LAT condensate nucleation underlie kinetic proofreading, enabling selective signaling responses to high-affinity pMHC ligands. The cooperativity in the nucleation and growth of LAT condensates also provides a mechanism to amplify weak signals from single foreign peptides and for condensates to grow with increasing antigen numbers. In contrast to other models, condensate-nucleation proofreading predicts a dependence of signal strength on pMHC spacing at fixed number, a prediction we validated experimentally using a protein scaffold to present pMHCs at defined intervals. Our results suggest that nucleation-condensation proofreading underlies the remarkable antigen detection capabilities of the TCR signaling pathway.