The structural diversity of natural sulfated glycosaminoglycans (GAGs) presents major promise for discovery of chemical biology tools or therapeutic agents. Yet, few GAGs have been identified so far to exhibit this promise. We reasoned that a simple approach to identify such GAGs is to explore sequences containing rare residues, for example, 2-O-sulfonated glucuronic acid (GlcAp2S). Genetic algorithm-based computational docking and filtering suggested that GlcAp2S containing heparan sulfate (HS) may exhibit highly selective recognition of antithrombin, a key plasma clot regulator. HS containing only GlcAp2S and 2-N-sulfonated glucosamine residues, labeled as HS2S2S, was chemoenzymatically synthesized in just two steps and was found to preferentially bind antithrombin over heparin cofactor II, a closely related serpin. Likewise, HS2S2S directly inhibited thrombin but not factor Xa, a closely related protease. The results show that a HS containing rare GlcAp2S residues exhibits the unusual property of selective antithrombin activation and direct thrombin inhibition. More importantly, HS2S2S is also the first molecule to activate antithrombin nearly as well as the heparin pentasaccharide although being completely devoid of the critical 3-O-sulfonate group. Thus, this work shows that novel functions and mechanisms may be uncovered by studying rare GAG residues/sequences.