Despite their importance for material and life sciences, multivalent interactions between polymers and surfaces remain poorly understood. Combining recent achievements of synthetic chemistry and surface characterization, we have developed a well-defined and highly specific model system based on host/guest interactions. We use this model to study the binding of hyaluronic acid functionalized with host molecules to tunable surfaces displaying different densities of guest molecules. Remarkably, we find that the surface density of bound polymer increases faster than linearly with the surface density of binding sites. Based on predictions from a simple analytical model, we propose that this superselective behavior arises from a combination of enthalpic and entropic effects upon binding of nanoobjects to surfaces, accentuated by the ability of polymer chains to interpenetrate.