Alloying provides a means by which to tune a metal catalyst's electronic structure and thus tailor its performance; however, mean-field behaviour in metals imposes limits. To access unprecedented catalytic behaviour, materials must exhibit emergent properties that are not simply interpolations of the constituent components' properties. Here we show an emergent electronic structure in single-atom alloys, whereby weak wavefunction mixing between minority and majority elements results in a free-atom-like electronic structure on the minority element. This unusual electronic structure alters the minority element's adsorption properties such that the bonding with adsorbates resembles the bonding in molecular metal complexes. We demonstrate this phenomenon with AgCu alloys, dilute in Cu, where the Cu d states are nearly unperturbed from their free-atom state. In situ electron spectroscopy demonstrates that this unusual electronic structure persists in reaction conditions and exhibits a 0.1 eV smaller activation barrier than bulk Cu in methanol reforming. Theory predicts that several other dilute alloys exhibit this phenomenon, which offers a design approach that may lead to alloys with unprecedented catalytic properties.