The present invention provides TCRs having high affinity. The TCR binds to SLYNTVATL (SEQ ID NO:16)-HLA-A*0201 with a KD of less than or equal to 1 μM and/or an off-rate (koff) of 1×10−3 S−1 or slower using Surface Plasmon Resonance. The TCRs are non-native, isolated or recombinant. The TCRs are useful, either alone, or with a therapeutic agent, for targeting HIV infected cells that present the SLYNTVATL (SEQ ID NO:16)-HLA-A*0201 complex.