Single-phase ${\mathrm{Au}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}$ alloys, with $0.3\ensuremath{\lesssim}x\ensuremath{\lesssim}0.5$, have been formed through solid-state interdiffusion of pure polycrystalline Au and La thin films (100-600 \AA{}) at temperatures of 50-80\ifmmode^\circ\else\textdegree\fi{}C. The reaction is driven by the large negative heat of mixing in the amorphous alloy and occurs at low temperatures by the anomalously fast diffusion of Au in La. The composition regime giving a single-phase amorphous product is explained with use of a free-energy diagram.