T cell receptors (TCR) have a low affinity for the MHC and the presented peptides (MHCpep). The low affinity of the TCR is crucial in T cell recognition and activation. Nevertheless, I propose that the TCR is perfectly capable of specifically binding MHCpep with high affinity. This hypothesis is supported by several data. Among them, the frequency of negatively selected immature T cells and of high affinity alloreactive T cells. Structural and functional analysis indicates that the TCR binding regions are quite similar to those of immunoglobulins. This implies similar binding strategies and suggests that there are no structural constraints on TCR affinity. The possible existence of high affinity TCR is relevant for current views on immune recognition, alloreactivity and peptide antagonism. In particular, it supports a model of immune recognition as unselected higher affinity binding to newly encountered peptides. The actual production of specific affinity TCR may also prove crucial for a soluble T cell receptor-based immunotherapy and for the co-crystallization of TCR with MHC and peptides.