A recently designed single-crystal surface calorimeter has been deployed to measure the energy difference between two solid surface structures. The clean Pt{100} surface is reconstructed to a stable phase in which the surface layer of platinum atoms has a quasi-hexagonal structure. By comparison of the heats of adsorption of CO and of C2H4 on this stable Pt{100}-hex phase with those on a metastable Pt(100)-(1 x 1) surface, the energy difference between the two clean phases was measured as 20 +/- 3 and 25 +/- 3 kilojoules per mole of surface platinum atoms.