Next-generation sequencing (NGS) machines can sequence millions of DNA strands in a single run, such as oligonucleotide (oligo) libraries comprising millions to trillions of discrete oligo sequences. Capillary electrophoresis is an attractive technique to select tight binding oligos or "aptamers" because it requires minimal sample volumes (e.g., 100 nL) and offers a solution-phase selection environment through which enrichment of target-binding oligos can be determined quantitatively. We describe here experiments using capillary transient isotachophoresis (ctITP)-based nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM) as a method for selecting aptamers from a randomized library containing a known (29mer) thrombin-binding aptamer. Our capillary electrophoresis (CE)-selected samples were sequenced by the Ion Torrent Personal Genome Machine (PGM) and analyzed for selection efficiency. We show that a single round of CE selection can enrich a randomer synthetic DNA oligo mixture for thrombin-binding activity from 0.4% aptamer content before selection to >15% aptamer content.