Aptamers, an emerging class of therapeutics, are DNA or RNA molecules that are selected to bind molecular targets that range from small organic compounds to large proteins. All of the determined structures of aptamers in complex with small molecule targets show that aptamers cage such ligands. In structures of aptamers in complex with proteins that naturally bind nucleic acid, the aptamers occupy the nucleic acid binding site and often mimic the natural interactions. Here we present a crystal structure of an RNA aptamer bound to human thrombin, a protein that does not naturally bind nucleic acid, at 1.9 A resolution. The aptamer, which adheres to thrombin at the binding site for heparin, presents an extended molecular surface that is complementary to the protein. Protein recognition involves the stacking of single-stranded adenine bases at the core of the tertiary fold with arginine side chains. These results exemplify how RNA aptamers can fold into intricate conformations that allow them to interact closely with extended surfaces on non-RNA binding proteins.