The T cell receptor (TCR) repertoire can provide a personalized biomarker for infectious and non-infectious diseases. We describe a protocol for amplifying, sequencing, and analyzing TCRs which is robust, sensitive, and versatile. The key experimental step is ligation of a single-stranded oligonucleotide to the 3′ end of the TCR cDNA. This allows amplification of all possible rearrangements using a single set of primers per locus. It also introduces a unique molecular identifier to label each starting cDNA molecule. This molecular identifier is used to correct for sequence errors and for effects of differential PCR amplification efficiency, thus producing more accurate measures of the true TCR frequency within the sample. This integrated experimental and computational pipeline is applied to the analysis of human memory and naive subpopulations, and results in consistent measures of diversity and inequality. After error correction, the distribution of TCR sequence abundance in all subpopulations followed a power law over a wide range of values. The power law exponent differed between naïve and memory populations, but was consistent between individuals. The integrated experimental and analysis pipeline we describe is appropriate to studies of T cell responses in a broad range of physiological and pathological contexts.