Tris(vancomycin carboxamide) binds a trivalent ligand derived from D-Ala-D-Ala with very high affinity : dissociation constant (K-d) approximate to 4 x 10(-17) +/- 1 x 10(-17) M. High-affinity trivalent binding and monovalent binding are fundamentally different. In trivalent (and more generally, polyvalent) binding, dissociation occurs in stages, and its rate can be accelerated by monovalent ligand at sufficiently high concentrations. In monovalent binding, dissociation is determined solely by the rate constant for dissociation and cannot be accelerated by added monomer. Calorimetric measurements for the trivalent system indicate an approximately additive gain in enthalpy relative to the corresponding monomers. This system is one of the most stable organic receptor-ligand pairs involving small molecules that is known. It illustrates the practicality of designing very high-affinity systems based on polyvalency.