Previously, we evolved a DNA polymerase, SFM4-3, for the recognition of substrates modified at their 2' positions with a fluoro, O-methyl, or azido substituent. Here we use SFM4-3 to synthesize 2'-azido-modified DNA; we then use the azido group to attach different, large hydrophobic groups via click chemistry. We show that SFM4-3 recognizes the modified templates under standard conditions, producing natural DNA and thereby allowing amplification. To demonstrate the utility of this remarkable property, we use SFM4-3 to select aptamers with large hydrophobic 2' substituents that bind human neutrophil elastase or the blood coagulation protein factor IXa. The results indicate that SFM4-3 should facilitate the discovery of aptamers that adopt novel and perhaps more protein-like folds with hydrophobic cores that in turn allow them to access novel activities.