Development of a self-tolerant T-cell receptor (TCR) repertoire with the potential to recognize the universe of infectious agents depends on proper regulation of TCR signalling. The repertoire is whittled down during T-cell development in the thymus by the ability of quasi-randomly generated TCRs to interact with self-peptides presented by major histocompatibility complex (MHC) proteins. Low-affinity TCR interactions with self-MHC proteins generate weak signals that initiate ‘positive selection’, causing maturation of CD4- or CD8αβ-expressing ‘single-positive’ thymocytes from CD4⁺CD8αβ⁺ ‘double-positive’ precursors. These develop into mature naive T cells of the secondary lymphoid organs. TCR interaction with high-affinity agonist self-ligands results in ‘negative selection’ by activation-induced apoptosis or ‘agonist selection’ of functionally differentiated self-antigen-experienced T cells^,. Here we show that positive selection is enabled by the ability of the T-cell-specific protein Themis^,,,,, to specifically attenuate TCR signal strength via SHP1 recruitment and activation in response to low- but not high-affinity TCR engagement. Themis acts as an analog-to-digital converter translating graded TCR affinity into clear-cut selection outcome. By dampening mild TCR signals Themis increases the affinity threshold for activation, enabling positive selection of T cells with a naive phenotype in response to low-affinity self-antigens.