Highly stable glasses of tris-naphthylbenzene transform into a liquid when annealed above the glass transition temperature T_{g}. In contrast to the predictions of standard models, the observed transformation is spatially inhomogeneous. Secondary ion mass spectrometry experiments on isotopically labeled multilayer films show that the liquid grows into the stable glass with sharp growth fronts initiated at the free surface and at the interface with the substrate. For the free surface, the growth velocity is constant in time and has the same temperature dependence as self-diffusion in the equilibrium supercooled liquid. These stable glasses are packed so efficiently that surfaces and interfaces are required to initiate the transformation to the liquid even well above T_{g}.