The T cell receptor is generated by a process of random and imprecise somatic recombination. The number of possible T cell receptors which this process can produce is enormous, greatly exceeding the number of T cells in an individual. Thus, the likelihood of identical TCRs being observed in multiple individuals (public TCRs) might be expected to be very low. Nevertheless such public TCRs have often been reported. In this study we explore the extent of TCR publicity in the context of acute resolving Lymphocytic choriomeningitis virus (LCMV) infection in mice. We show that the repertoire of effector T cells following LCMV infection contains a population of highly shared TCR sequences. This subset of TCRs has a distribution of naive precursor frequencies, generation probabilities, and physico-chemical CDR3 properties which lie between those of classic public TCRs, which are observed in uninfected repertoires, and the dominant private TCR repertoire. We have named this set of sequences “hidden public” TCRs, since they are only revealed following infection. A similar repertoire of hidden public TCRs can be observed in humans after a first exposure to SARS-COV-2. The presence of hidden public TCRs which rapidly expand following viral infection may therefore be a general feature of adaptive immunity, identifying an additional level of inter-individual sharing in the TCR repertoire which may form an important component of the effector and memory response.