There is a critical need for improved methane-oxidation catalysts to both reduce emissions of methane, a greenhouse gas, and improve the performance of gas turbines. However, materials that are currently available either have low activity below 400 degrees C or are unstable at higher temperatures. Here, we describe a supramolecular approach in which single units composed of a palladium (Pd) core and a ceria (CeO2) shell are preorganized in solution and then homogeneously deposited onto a modified hydrophobic alumina. Electron microscopy and other structural methods revealed that the Pd cores remained isolated even after heating the catalyst to 850 degrees C. Enhanced metal-support interactions led to exceptionally high methane oxidation, with complete conversion below 400 degrees C and outstanding thermal stability under demanding conditions.